List of Indian inventions and discoveries

<h2 id="ancient-india">Ancient India</h2>
See also: <a href="/facts/History_of_science_and_technology_in_the_Indian_subcontinent/BhwzGDTn">History of science and technology in the Indian subcontinent</a>, <a href="/facts/List_of_inventions_and_discoveries_of_the_Indus_Valley_Civilisation/pY51lde7">List of inventions and discoveries of the Indus Valley Civilisation</a>, and <a href="/facts/Timeline_of_Indian_innovation/v7UrKG1y">Timeline of Indian innovation</a>
<h3>Agriculture</h3>
<ul><li><a href="/facts/Indigo/0gteqpM1">Indigo dye</a> – Indigo, a blue pigment and a dye, was used in India, which was also the earliest major centre for its production and processing.<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a> The Indigofera tinctoria variety of Indigo was domesticated in India.<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a> Indigo, used as a dye, made its way to the <a href="/facts/Ancient_Greece/PTVBrWXq">Greeks</a> and the <a href="/facts/Ancient_Rome/cGqIuxPd">Romans</a> via various trade routes, and was valued as a luxury product.<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a></li>
<li><a href="/facts/Jute/33l9lhI9">Jute cultivation</a> – Jute has been cultivated in India since ancient times.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> Raw jute was exported to the <a href="/facts/Western_world/UQl4e7du">western world</a>, where it was used to make <a href="/facts/Rope/heTalcCM">ropes</a> and cordage.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> The Indian jute industry, in turn, was modernised during the British Raj in India.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> The region of <a href="/facts/Bengal/xp3t2Dyd">Bengal</a> was the major centre for Jute cultivation, and remained so before the modernisation of India's jute industry in 1855, when <a href="/facts/Kolkata/k0HVgEYm">Kolkata</a> became a centre for jute processing in India.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a></li>
<li><a href="/facts/Sugar/jb5KXRHT">Sugar</a> – Sugarcane was originally from tropical <a href="/facts/South_Asia/7gTqe3hY">South Asia</a> and <a href="/facts/Southeast_Asia/VafwT517">Southeast Asia</a>,<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> with different species originating in India, and S. edule and S. officinarum from <a href="/facts/New_Guinea/qB0bzfSH">New Guinea</a>.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> The process of producing crystallised sugar from sugar cane, in India, dates to at least the beginning of the common era, with 1st century CE Greek and Roman authors writing on Indian sugar.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a><a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> The process was soon transmitted to China with travelling Buddhist monks.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a> Chinese documents confirm at least two missions to India, initiated in 647 CE, for obtaining technology for sugar-refining.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a> Each mission returned with results on refining sugar.<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a></li></ul>
<h3>Construction, civil engineering and architecture</h3>

<ul><li><a href="/facts/Stepwell/c70o4NCA">Stepwell</a> – While the early history of stepwells is poorly understood, water structures in Western India were their likely predecessor.<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a> The three features of stepwells in the subcontinent are evident from one particular site, abandoned by 2500 BCE, which combines a bathing pool, steps leading down to water, and figures of some religious importance into one structure.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a></li>
<li><a href="/facts/Stupa/0dXQxGA3">Stupa</a> – The origin of the stupa can be traced to 3rd-century BCE India.<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a> It was used as a commemorative monument associated with storing sacred relics.<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a> The stupa architecture was adopted in <a href="/facts/Southeast_Asia/VafwT517">Southeast</a> and <a href="/facts/East_Asia/D8yGVCQX">East Asia</a>, where it evolved into the <a href="/facts/Pagoda/KekTlSK1">pagoda</a>, a Buddhist monument used for enshrining sacred relics.<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a></li>
<li>Residential <a href="/facts/University/skaJt2Io">University</a> – <a href="/facts/Nalanda/ATdoGwUE">Nalanda</a> (Nālandā, pronounced [naːlən̪d̪aː]) was a renowned <a href="/facts/Mahavihara/nnJUGCJP">mahavihara</a> (<a href="/facts/Buddhism/G0wsjrSl">Buddhist</a> monastic university) in ancient <a href="/facts/Magadha_(Mahajanapada)/e2vLVE9U">Magadha</a> (modern-day <a href="/facts/Bihar/T5Ga9JF8">Bihar</a>), eastern <a href="/facts/India/QW4TV4sy">India</a>.<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a><a class="footnote-ref" id="fnref:22" href="#fn:22">22</a><a class="footnote-ref" id="fnref:23" href="#fn:23">23</a> Considered by historians to be the world's first residential university<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a> and among the greatest centres of learning in the ancient world, it was located near the city of Rajagriha (now <a href="/facts/Rajgir/pUD55c6k">Rajgir</a>) and about 90 kilometres (56 mi) southeast of Pataliputra (now <a href="/facts/Patna/paEkUEgr">Patna</a>) and operated from 427 until 1197 CE.<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a></li></ul>
<h3>Finance and banking</h3>
<ul><li><a href="/facts/Cheque/AmS09zUa">Cheque/Check</a> – There is early evidence of using cheques/checks. In India, during the <a href="/facts/Maurya_Empire/STQagR1r">Maurya Empire</a> (from 321 to 185 BC), a commercial instrument called the "Adesha" was in use, which was an order on a banker desiring him to pay the money of the note to a third person (now known as or referred to as a "Negotiable Instrument").<a class="footnote-ref" id="fnref:26" href="#fn:26">26</a></li></ul>
<h3>Games</h3>
Main article: <a href="/facts/Traditional_games_of_South_Asia/F6AlL88K">Traditional games of South Asia</a>
<ul><li><a href="/facts/Atya-patya/4B0opgzJ">Atya-patya</a> – This variation of tag was being played as early as 100 CE, and was possibly invented by farmers as a way of practicing driving away birds. It was later used as a form of military training in <a href="/facts/Kerala/DMP5u40q">Kerala</a> in close relation to the martial art of <a href="/facts/Kalaripayattu/CsUfXjeU">kalaripayattu</a>.<a class="footnote-ref" id="fnref:27" href="#fn:27">27</a></li>
<li><a href="/facts/Blindfold_chess/Qhr4vVyA">Blindfold chess</a> – <a href="/facts/List_of_games_that_Buddha_would_not_play/Xo7HuJIT">Games prohibited by Buddha</a> includes a variant of ashtapada game played on imaginary boards. Akasam astapadam was an ashtapada variant played with no board, literally "astapadam played in the sky". A correspondent in the <a href="/facts/American_Chess_Bulletin/T6zQ9VM1">American Chess Bulletin</a> identifies this as likely the earliest literary mention of a blindfold chess variant.<a class="footnote-ref" id="fnref:28" href="#fn:28">28</a></li>
<li><a href="/facts/Carrom/5ERJjNNc">Carrom</a> – The game of carrom originated in <a href="/facts/India/QW4TV4sy">India</a>.<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a> One carrom board with its surface made of glass is still available in one of the palaces in <a href="/facts/Patiala%2c_India/b1RmtIoI">Patiala, India</a>.<a class="footnote-ref" id="fnref:30" href="#fn:30">30</a> It became very popular among the masses after <a href="/facts/World_War_I/vITTUanQ">World War I</a>. State-level competitions were being held in the different states of India during the early part of the twentieth century. Serious carrom tournaments may have begun in <a href="/facts/Sri_Lanka/VtTBmysE">Sri Lanka</a> in 1935 but by 1958, both India and Sri Lanka had formed official federations of carrom clubs, sponsoring tournaments and awarding prizes.<a class="footnote-ref" id="fnref:31" href="#fn:31">31</a></li>
<li><a href="/facts/Chaturanga/P6x2SD7G">Chaturanga</a> – The precursor of <a href="/facts/Chess/47ykvkHF">chess</a> originated in India during the <a href="/facts/Gupta_dynasty/KbMVInGv">Gupta dynasty</a> (c. 280–550 CE).<a class="footnote-ref" id="fnref:32" href="#fn:32">32</a><a class="footnote-ref" id="fnref:33" href="#fn:33">33</a><a class="footnote-ref" id="fnref:34" href="#fn:34">34</a><a class="footnote-ref" id="fnref:35" href="#fn:35">35</a> Both the <a href="/facts/Persian_people/4GhM3jl2">Persians</a> and <a href="/facts/Arab/E77duPsg">Arabs</a> ascribe the origins of the game of Chess to the Indians.<a class="footnote-ref" id="fnref:36" href="#fn:36">36</a><a class="footnote-ref" id="fnref:37" href="#fn:37">37</a><a class="footnote-ref" id="fnref:38" href="#fn:38">38</a> The words for "chess" in <a href="/facts/Old_Persian/gxx47Ul7">Old Persian</a> and <a href="/facts/Arabic/A1e66hVV">Arabic</a> are chatrang and <a href="/facts/Shatranj/GT5JRl3A">shatranj</a> respectively – terms derived from <a href="/facts/Chaturanga/P6x2SD7G">caturaṅga</a> in <a href="/facts/Sanskrit/ychfjhlx">Sanskrit</a>,<a class="footnote-ref" id="fnref:39" href="#fn:39">39</a><a class="footnote-ref" id="fnref:40" href="#fn:40">40</a> which literally means an army of four divisions or four corps.<a class="footnote-ref" id="fnref:41" href="#fn:41">41</a><a class="footnote-ref" id="fnref:42" href="#fn:42">42</a> Chess spread throughout the world and many variants of the game soon began taking shape.<a class="footnote-ref" id="fnref:43" href="#fn:43">43</a> This game was introduced to the <a href="/facts/Near_East/gD1vyGQI">Near East</a> from India and became a part of the princely or courtly education of <a href="/facts/Persian_Empire/avlzWxF0">Persian</a> nobility.<a class="footnote-ref" id="fnref:44" href="#fn:44">44</a> <a href="/facts/Buddhist/G0wsjrSl">Buddhist</a> pilgrims, <a href="/facts/Silk_Road/TLBryY39">Silk Road</a> traders and others carried it to the <a href="/facts/Far_East/wHcmLNM5">Far East</a> where it was transformed and assimilated into a game often played on the intersection of the lines of the board rather than within the squares.<a class="footnote-ref" id="fnref:45" href="#fn:45">45</a> Chaturanga reached Europe through Persia, the <a href="/facts/Byzantine_empire/njEELXWF">Byzantine empire</a> and the expanding <a href="/facts/Arabian/x1fDka2b">Arabian</a> empire.<a class="footnote-ref" id="fnref:46" href="#fn:46">46</a><a class="footnote-ref" id="fnref:47" href="#fn:47">47</a> <a href="/facts/Muslims/W2ukq4pg">Muslims</a> carried Shatranj to <a href="/facts/North_Africa/ItxQAfs7">North Africa</a>, <a href="/facts/Sicily/E6fug03z">Sicily</a>, and Spain by the 10th century where it took its final modern form of chess.<a class="footnote-ref" id="fnref:48" href="#fn:48">48</a></li>
<li><a href="/facts/Kabaddi/GRIzCtxk">Kabaddi</a> – The game of kabaddi originated in India during prehistory.<a class="footnote-ref" id="fnref:49" href="#fn:49">49</a> Suggestions on how it evolved into the modern form range from wrestling exercises, military drills, and collective self-defence but most authorities agree that the game existed in some form or the other in India during the period between 1500 and 400 BCE.<a class="footnote-ref" id="fnref:50" href="#fn:50">50</a></li>
<li><a href="/facts/Kalaripayattu/CsUfXjeU">Kalaripayattu</a> – One of the world's oldest form of martial arts is <a href="/facts/Kalaripayattu/CsUfXjeU">Kalaripayattu</a> that developed in the southwest state of <a href="/facts/Kerala/DMP5u40q">Kerala</a> in India.<a class="footnote-ref" id="fnref:51" href="#fn:51">51</a> It is believed to be the oldest surviving martial art in India, with a history spanning over 3,000 years.<a class="footnote-ref" id="fnref:52" href="#fn:52">52</a></li>
<li><a href="/facts/Kho-kho/WIDAUpxc">Kho-kho</a> – This is one of the oldest variations of <a href="/facts/Tag_(game)/lNgXc04t">tag</a> in the world, having been played since as early as the fourth century BCE.<a class="footnote-ref" id="fnref:53" href="#fn:53">53</a></li>
<li><a href="/facts/Ludo_(board_game)/hIKxwD1B">Ludo</a> – <a href="/facts/Pachisi/J5ILMSGN">Pachisi</a> originated in India by the 6th century.<a class="footnote-ref" id="fnref:54" href="#fn:54">54</a> The earliest evidence of this game in India is the depiction of boards on the caves of Ajanta.<a class="footnote-ref" id="fnref:55" href="#fn:55">55</a> A variant of this game, called Ludo, made its way to England during the British Raj.<a class="footnote-ref" id="fnref:56" href="#fn:56">56</a></li>
<li><a href="/facts/Mallakhamba/RrnzYAKS">Mallakhamba</a> – It is a traditional sport, originating from the <a href="/facts/Indian_subcontinent/0XUWGXpx">Indian subcontinent</a>, in which a <a href="/facts/Gymnast/YaX3BFwW">gymnast</a> performs aerial <a href="/facts/Yoga/HrhU9JdW">yoga</a> or <a href="/facts/Gymnastic/YaX3BFwW">gymnastic</a> postures and <a href="/facts/Wrestling/mTFzecQw">wrestling</a> grips in concert with a vertical stationary or hanging wooden pole, cane, or rope.The earliest literary known mention of Mallakhamb is in the 1135 CE Sanskrit classic <a href="/facts/Manasollasa/o9JtX1lN">Manasollasa</a>, written by <a href="/facts/Someshvara_III/fJbRtvTm">Someshvara III</a>. It has been thought to be the ancestor of <a href="/facts/Pole_dance/LvKqNtsc">Pole Dancing</a>.</li>
<li><a href="/facts/Nuntaa_(game)/XJvNMIkV">Nuntaa</a>, also known as Kutkute.<a class="footnote-ref" id="fnref:57" href="#fn:57">57</a></li>
<li><a href="/facts/Seven_stones/QnYS1SMb">Seven stones</a> – An Indian subcontinent game also called Pitthu is played in rural areas has its origins in the Indus Valley Civilization.<a class="footnote-ref" id="fnref:58" href="#fn:58">58</a></li>
<li><a href="/facts/Snakes_and_ladders/uIWtQ6j6">Snakes and ladders</a> – Vaikunta pali Snakes and ladders originated in India as a game based on morality.<a class="footnote-ref" id="fnref:59" href="#fn:59">59</a> During British rule of India, this game made its way to England, and was eventually introduced in the United States of America by game-pioneer <a href="/facts/Milton_Bradley/KWBUXTcJ">Milton Bradley</a> in 1943.<a class="footnote-ref" id="fnref:60" href="#fn:60">60</a></li>
<li><a href="/facts/Suit_(cards)/JJlSk2Pr">Suits</a> game: Kridapatram is an early <a href="/facts/Suit_(cards)/JJlSk2Pr">suits</a> game, made of painted rags, invented in Ancient India. The term kridapatram literally means "painted rags for playing."<a class="footnote-ref" id="fnref:61" href="#fn:61">61</a><a class="footnote-ref" id="fnref:62" href="#fn:62">62</a><a class="footnote-ref" id="fnref:63" href="#fn:63">63</a><a class="footnote-ref" id="fnref:64" href="#fn:64">64</a><a class="footnote-ref" id="fnref:65" href="#fn:65">65</a> Paper playing cards first appeared in East Asia during the 9th century.<a class="footnote-ref" id="fnref:66" href="#fn:66">66</a><a class="footnote-ref" id="fnref:67" href="#fn:67">67</a> The medieval Indian game of <a href="/facts/Ganjifa/3GMJ6GXh">ganjifa</a>, or playing cards, is first recorded in the 16th century.<a class="footnote-ref" id="fnref:68" href="#fn:68">68</a></li>
<li><a href="/facts/Vajra-mushti/Rdx7jPJn">Vajra-mushti</a> – refers to a wrestling where <a href="/facts/Knuckleduster/GtFtC5UA">knuckleduster</a> like weapon is employed.The first literary mention of vajra-musti comes from the Manasollasa of the <a href="/facts/Chalukya/kfwnEMqT">Chalukya</a> king Someswara III (1124–1138), although it has been conjectured to have existed since as early as the <a href="/facts/Maurya_Empire/STQagR1r">Maurya dynasty</a><a class="footnote-ref" id="fnref:69" href="#fn:69">69</a><a class="footnote-ref" id="fnref:70" href="#fn:70">70</a></li></ul>
<h3>Textile and material production</h3>
<ul><li><a href="/facts/Button_(clothing)/KwJJoP3o">Button</a> – Ornamental buttons—made from <a href="/facts/Seashell/5AyVlBwo">seashell</a>—were used in the <a href="/facts/Indus_Valley_civilization/6xM4aK23">Indus Valley civilization</a> for ornamental purposes by 2000 BCE.<a class="footnote-ref" id="fnref:71" href="#fn:71">71</a> Some buttons were carved into geometric shapes and had holes pierced into them so that they could be attached to clothing by using a thread.<a class="footnote-ref" id="fnref:72" href="#fn:72">72</a> Ian McNeil (1990) holds that: "The button, in fact, was originally used more as an ornament than as a fastening, the earliest known being found at Mohenjo-daro in the <a href="/facts/Indus_Valley/7vTRHA4t">Indus Valley</a>. It is made of a curved shell and about 5000 years old."<a class="footnote-ref" id="fnref:73" href="#fn:73">73</a></li></ul>

<ul><li><a href="/facts/Calico_(textile)/kaPyU0d6">Calico</a> – Calico had originated in the subcontinent by the 11th century and found mention in Indian literature, by the 12th-century writer Hemachandra. He has mentioned calico fabric prints done in a lotus design.<a class="footnote-ref" id="fnref:74" href="#fn:74">74</a> The Indian textile merchants traded in calico with the Africans by the 15th century and calico fabrics from <a href="/facts/Gujarat/HwmVfMwr">Gujarat</a> appeared in <a href="/facts/Egypt/8Ttg0JwB">Egypt</a>.<a class="footnote-ref" id="fnref:75" href="#fn:75">75</a> Trade with Europe followed from the 17th century onward.<a class="footnote-ref" id="fnref:76" href="#fn:76">76</a> Within India, calico originated in <a href="/facts/Kozhikode/XarhNNKU">Kozhikode</a>.<a class="footnote-ref" id="fnref:77" href="#fn:77">77</a></li>
<li><a href="/facts/Carding/qePnkTr8">Carding devices</a> – Historian of science <a href="/facts/Joseph_Needham/lC1qJAuI">Joseph Needham</a> ascribes the invention of bow-instruments used in textile technology to India.<a class="footnote-ref" id="fnref:78" href="#fn:78">78</a> The earliest evidence for using bow-instruments for carding comes from India (2nd century CE).<a class="footnote-ref" id="fnref:79" href="#fn:79">79</a> These carding devices, called kaman and dhunaki would loosen the texture of the fibre by the means of a vibrating string.<a class="footnote-ref" id="fnref:80" href="#fn:80">80</a></li>
<li><a href="/facts/Cashmere_wool/LCFy5UXU">Cashmere</a> – The fibre cashmere fibre also known as pashm or pashmina for its use in <a href="/facts/Kashmir_shawl/UUrjAygB">the handmade shawls of Kashmir, India</a>.<a class="footnote-ref" id="fnref:81" href="#fn:81">81</a> The woolen shawls made from wool in Indian administered <a href="/facts/Kashmir/Rok34JM5">Kashmir</a> find written mention between the 3rd century BCE and the 11th century CE.<a class="footnote-ref" id="fnref:82" href="#fn:82">82</a></li>
<li><a href="/facts/Spinning_wheel/wAVuEYlF">Charkha</a> (Spinning wheel): invented in India, between 500 and 1000 CE.<a class="footnote-ref" id="fnref:83" href="#fn:83">83</a></li>
<li><a href="/facts/Chintz/E2SzHJcI">Chintz</a> – The origin of Chintz is from the printed all cotton fabric of calico in India.<a class="footnote-ref" id="fnref:84" href="#fn:84">84</a> The origin of the word chintz itself is from the <a href="/facts/Hindi_language/n1QIEeCC">Hindi language</a> word चित्र् (chitr), which means an image.<a class="footnote-ref" id="fnref:85" href="#fn:85">85</a><a class="footnote-ref" id="fnref:86" href="#fn:86">86</a></li>
<li><a href="/facts/Cotton/efXRcjbn">Cotton cultivation</a> – Cotton was cultivated by the inhabitants of the <a href="/facts/Indus_Valley_civilisation/6xM4aK23">Indus Valley civilisation</a> by the <a href="/facts/5th_millennium_BCE/UGAYsP0f">5th millennium BCE</a> – <a href="/facts/4th_millennium_BCE/IRr7dCr1">4th millennium BCE</a>.<a class="footnote-ref" id="fnref:87" href="#fn:87">87</a> The Indus cotton industry was well developed and some methods used in cotton spinning and fabrication continued to be practised until the modern industrialisation of India.<a class="footnote-ref" id="fnref:88" href="#fn:88">88</a> Well before the <a href="/facts/Common_Era/e5DpqUoe">Common Era</a>, the use of cotton textiles had spread from India to the <a href="/facts/Mediterranean/Vr2pzVbM">Mediterranean</a> and beyond.<a class="footnote-ref" id="fnref:89" href="#fn:89">89</a></li>
<li><a href="/facts/Cotton_gin/hAYQ3NLV">Single roller cotton gin</a> – The <a href="/facts/Ajanta_Caves/I8Kkk1Ug">Ajanta Caves</a> of India yield evidence of a single roller cotton gin in use by the 5th century.<a class="footnote-ref" id="fnref:90" href="#fn:90">90</a> This cotton gin was used in India until innovations were made in form of foot powered gins.<a class="footnote-ref" id="fnref:91" href="#fn:91">91</a> The cotton gin was invented in India as a mechanical device known as charkhi, more technically the "wooden-worm-worked roller". This mechanical device was, in some parts of India, driven by water power.<a class="footnote-ref" id="fnref:92" href="#fn:92">92</a></li>
<li><a href="/facts/Worm_drive/h2mcUHge">Worm drive</a> <a href="/facts/Cotton_gin/hAYQ3NLV">cotton gin</a> – The worm drive later appeared in the <a href="/facts/Indian_subcontinent/0XUWGXpx">Indian subcontinent</a>, for use in roller <a href="/facts/Cotton_gin/hAYQ3NLV">cotton gins</a>, during the <a href="/facts/Delhi_Sultanate/19oLzpBF">Delhi Sultanate</a> in the thirteenth or fourteenth centuries.<a class="footnote-ref" id="fnref:93" href="#fn:93">93</a></li>
<li><a href="/facts/Crank_(mechanism)/1a3bCxyE">Crank</a> Handle <a href="/facts/Cotton_Gin/hAYQ3NLV">Cotton Gin</a> – The incorporation of the <a href="/facts/Crank_(mechanism)/1a3bCxyE">crank</a> handle in the cotton gin, first appeared in either the late <a href="/facts/Delhi_Sultanate/19oLzpBF">Delhi Sultanate</a> or the early <a href="/facts/Mughal_Empire/yRg2kAy5">Mughal Empire</a>.<a class="footnote-ref" id="fnref:94" href="#fn:94">94</a></li>
<li><a href="/facts/Palampore/x3jhG557">Palampore</a> – पालमपोर् (Hindi language) of Indian origin<a class="footnote-ref" id="fnref:95" href="#fn:95">95</a> was imported to the western world—notable England and <a href="/facts/Colonial_America/6fYe7RfF">Colonial America</a>—from India.<a class="footnote-ref" id="fnref:96" href="#fn:96">96</a><a class="footnote-ref" id="fnref:97" href="#fn:97">97</a> In 17th-century England these hand painted cotton fabrics influenced native crewel work design.<a class="footnote-ref" id="fnref:98" href="#fn:98">98</a> Shipping vessels from India also took palampore to colonial America, where it was used in <a href="/facts/Quilting/gyhPr0Hx">quilting</a>.<a class="footnote-ref" id="fnref:99" href="#fn:99">99</a></li>
<li><a href="/facts/Prayer_flags/TDJw0KKz">Prayer flags</a> – The <a href="/facts/Buddhism/G0wsjrSl">Buddhist</a> <a href="/facts/S%25C5%25ABtra/2fuurf3z">sūtras</a>, written on cloth in India, were transmitted to other regions of the world.<a class="footnote-ref" id="fnref:100" href="#fn:100">100</a> These sutras, written on banners, were the origin of prayer flags.<a class="footnote-ref" id="fnref:101" href="#fn:101">101</a> Legend ascribes the origin of the prayer flag to the <a href="/facts/Shakyamuni_Buddha/8UchTM1s">Shakyamuni Buddha</a>, whose prayers were written on battle flags used by the <a href="/facts/Deva_(Buddhism)/b0RU5mu6">devas</a> against their adversaries, the <a href="/facts/Asura_(Buddhism)/mnewPuxH">asuras</a>.<a class="footnote-ref" id="fnref:102" href="#fn:102">102</a> The legend may have given the Indian <a href="/facts/Bhikku/AX9w7Y1a">bhikku</a> a reason for carrying the 'heavenly' banner as a way of signyfying his commitment to <a href="/facts/Ahimsa/gV8J0KQI">ahimsa</a>.<a class="footnote-ref" id="fnref:103" href="#fn:103">103</a> This knowledge was carried into <a href="/facts/Tibet/NQChzGo9">Tibet</a> by 800 CE, and the actual flags were introduced no later than 1040 CE, where they were further modified.<a class="footnote-ref" id="fnref:104" href="#fn:104">104</a> The Indian monk <a href="/facts/Atisha/zXaz5UME">Atisha</a> (980–1054 CE) introduced the Indian practice of printing on cloth prayer flags to Tibet.<a class="footnote-ref" id="fnref:105" href="#fn:105">105</a></li>
<li><a href="/facts/Shellac/VNRrGF0r">Shellac</a> - a biopolymer resin that is secreted by an insect called <a href="/facts/Kerria_lacca/z3IhGwRA">lac bug</a> onto tree trunks, it has multiple uses such as wood polishing, drug coating, candies etc. its name is derived from <a href="/facts/Lakh/FTocP0hn">lakh</a> word.</li>
<li><a href="/facts/Tanning_(leather)/NqL8LFrg">Tanning (leather)</a> – Ancient civilizations used leather for <a href="/facts/Waterskin/Hmblh5kl">waterskins</a>, bags, harnesses and tack, boats, <a href="/facts/Armour/jTpqE3du">armour</a>, <a href="/facts/Quiver/zynLDTry">quivers</a>, <a href="/facts/Scabbard/a709xnr7">scabbards</a>, <a href="/facts/Boot/k3vtmnUW">boots</a>, and <a href="/facts/Sandal_(footwear)/F4503auG">sandals</a>. Tanning was being carried out by the inhabitants of <a href="/facts/Mehrgarh/7JfFIqW5">Mehrgarh</a> in Ancient India between 7000 and 3300 BCE.<a class="footnote-ref" id="fnref:106" href="#fn:106">106</a></li>
<li>Roller <a href="/facts/Sugar_mill/nKe9VAcm">sugar mill</a> – Geared sugar <a href="/facts/Roller_mill/LHrc1J0h">rolling mills</a> first appeared in Mughal India, using the principle of rollers as well as <a href="/facts/Worm_gear/HYg3hKFG">worm gearing</a>, by the 17th century.<a class="footnote-ref" id="fnref:107" href="#fn:107">107</a></li></ul>
<h3>Well-being</h3>
See also: <a href="/facts/Indian_physical_culture/4I26XUS4">Indian physical culture</a>
<ul><li><a href="/facts/Indian_club/YR1lI9FS">Indian clubs</a>: The Indian club—which appeared in Europe during the 18th century—was used long by India's native soldiery before its introduction to Europe.<a class="footnote-ref" id="fnref:108" href="#fn:108">108</a> During the <a href="/facts/British_Raj/hBe6wvPS">British Raj</a> the British officers in India performed calisthenic exercises with clubs to keep in physical condition.<a class="footnote-ref" id="fnref:109" href="#fn:109">109</a> From Britain the use of club swinging spread to the rest of the world.<a class="footnote-ref" id="fnref:110" href="#fn:110">110</a></li>
<li><a href="/facts/Shampoo/ww9bFmT2">Shampoo</a> – The word shampoo in English is derived from <a href="/facts/Hindustani_language/rPnbEyYP">Hindustani</a> cā̃po (चाँपो IPA: [tʃãːpoː]),<a class="footnote-ref" id="fnref:111" href="#fn:111">111</a> and dates to 1762.<a class="footnote-ref" id="fnref:112" href="#fn:112">112</a> A variety of herbs and their extracts were used as shampoos since ancient times in India, evidence of early herbal shampoo have been discovered from Indus Valley Civilization site of Banawali dated to 2750–2500 BCE.<a class="footnote-ref" id="fnref:113" href="#fn:113">113</a> A very effective early shampoo was made by boiling <a href="/facts/Sapindus/vdmKL7vz">Sapindus</a> with dried <a href="/facts/Indian_gooseberry/M0uYlba1">Indian gooseberry</a> (aamla) and a few other herbs, using the strained extract. Sapindus, also known as soapberries or soapnuts, is called Ksuna (Sanskrit: क्षुण)<a class="footnote-ref" id="fnref:114" href="#fn:114">114</a> in ancient Indian texts and its fruit pulp contain saponins, a natural surfactant. The extract of Ksuna, creates a lather which Indian texts identify as phenaka (Sanskrit: फेनक),<a class="footnote-ref" id="fnref:115" href="#fn:115">115</a> leaves the hair soft, shiny and manageable. Other products used for hair cleansing were shikakai (<a href="/facts/Acacia_concinna/Sk0p5naw">Acacia concinna</a>), soapnuts (<a href="/facts/Sapindus/vdmKL7vz">Sapindus</a>), <a href="/facts/Hibiscus/j2IPaF6X">hibiscus</a> flowers,<a class="footnote-ref" id="fnref:116" href="#fn:116">116</a><a class="footnote-ref" id="fnref:117" href="#fn:117">117</a> ritha (<a href="/facts/Sapindus_mukorossi/uIUclfbd">Sapindus mukorossi</a>) and arappu (Albizzia amara).<a class="footnote-ref" id="fnref:118" href="#fn:118">118</a> <a href="/facts/Guru_Nanak/WlaxsDrN">Guru Nanak</a>, the founding prophet and the first <a href="/facts/Sikh_Guru/G8UIrbYC">Guru</a> of <a href="/facts/Sikhism/obh7aQIr">Sikhism</a>, made references to soapberry tree and soap in 16th century.<a class="footnote-ref" id="fnref:119" href="#fn:119">119</a> Washing of hair and body massage (champu) during a daily strip wash was an indulgence of early colonial traders in India. When they returned to Europe, they introduced their newly learnt habits, including the hair treatment they called shampoo.<a class="footnote-ref" id="fnref:120" href="#fn:120">120</a></li>
<li><a href="/facts/Yoga/HrhU9JdW">Yoga</a> – Yoga as a physical, mental, and spiritual practice originated in <a href="/facts/Ancient_India/ntYkAYDQ">ancient India</a>.<a class="footnote-ref" id="fnref:121" href="#fn:121">121</a></li></ul>
<h3>Medicine</h3>

<ul><li><a href="/facts/Angina_pectoris/rT1brdwS">Angina pectoris</a> – The condition was named "hritshoola" in ancient India and was described by <a href="/facts/Sushruta/2Sv4aBev">Sushruta</a> (6th century BCE).<a class="footnote-ref" id="fnref:122" href="#fn:122">122</a></li>
<li><a href="/facts/Ayurveda/XCgFAdb3">Ayurvedic</a> and <a href="/facts/Siddha_medicine/Cluo11T3">Siddha medicine</a> – Ayurveda and Siddha are ancient systems of medicine practised in South Asia. Ayurvedic ideas can be found in the Hindu text<a class="footnote-ref" id="fnref:123" href="#fn:123">123</a> (mid-first millennium BCE). Ayurveda has evolved over thousands of years, and is still practised today. In an internationalised form, it can be thought of as a <a href="/facts/Complementary_and_alternative_medicine/XwFG5qtK">complementary and alternative medicine</a>. In village settings, away from urban centres, it is simply "medicine." The Sanskrit word आयुर्वेदः (āyur-vedaḥ) means "knowledge (veda) for longevity (āyur)".<a class="footnote-ref" id="fnref:124" href="#fn:124">124</a> Siddha medicine is mostly prevalent in South India, and is transmitted in Tamil, not Sanskrit, texts. Herbs and minerals are basic raw materials of the Siddha therapeutic system whose origins may be dated to the early centuries CE.<a class="footnote-ref" id="fnref:125" href="#fn:125">125</a><a class="footnote-ref" id="fnref:126" href="#fn:126">126</a></li>
<li><a href="/facts/Diabetes/2xeHXbsI">Diabetes</a>: Physicians <a href="/facts/Sushruta/2Sv4aBev">Sushruta</a> and <a href="/facts/Charaka/UgNYnA2W">Charaka</a> distinguished the two different types of diabetes, which is latter dubbed as <a href="/facts/Type_1_diabetes/IkuQadGx">Type I</a> and <a href="/facts/Type_2_diabetes/zCMXksmt">Type II</a> diabetes.<a class="footnote-ref" id="fnref:127" href="#fn:127">127</a><a class="footnote-ref" id="fnref:128" href="#fn:128">128</a><a class="footnote-ref" id="fnref:129" href="#fn:129">129</a><a class="footnote-ref" id="fnref:130" href="#fn:130">130</a><a class="footnote-ref" id="fnref:131" href="#fn:131">131</a></li>
<li><a href="/facts/Leprosy/FSjTpMEB">Leprosy</a>: Kearns & Nash (2008) state that the first mention of leprosy is described in the Indian medical treatise <a href="/facts/Sushruta_Samhita/GPSYEjCs">Sushruta Samhita</a> (6th century BCE).<a class="footnote-ref" id="fnref:132" href="#fn:132">132</a> However, The Oxford Illustrated Companion to Medicine holds that the mention of leprosy, as well as ritualistic cures for it, were described in the <a href="/facts/Atharva-veda/21Nq9UIk">Atharva-veda</a> (1500–1200 BCE), written before the Sushruta Samhita.<a class="footnote-ref" id="fnref:133" href="#fn:133">133</a></li>
<li><a href="/facts/Calculus_(medicine)/qSjNdCY5">Lithiasis treatment</a> – The earliest operation for treating lithiasis, or the formations of stones in the body, is also given in the Sushruta Samhita (6th century BCE).<a class="footnote-ref" id="fnref:134" href="#fn:134">134</a> The operation involved exposure and going up through the floor of the bladder.<a class="footnote-ref" id="fnref:135" href="#fn:135">135</a></li>
<li><a href="/facts/Visceral_leishmaniasis/bu6ne799">Visceral leishmaniasis, treatment of</a> – The Indian (Bengali) medical practitioner <a href="/facts/Upendranath_Brahmachari/EWVnzAHI">Upendranath Brahmachari</a> (19 December 1873 – 6 February 1946) was nominated for the <a href="/facts/Nobel_Prize_in_Physiology_or_Medicine/rlnpJX84">Nobel Prize in Physiology or Medicine</a> in 1929 for his discovery of 'ureastibamine (<a href="/facts/Antimony/YsA7lVgT">antimonial</a> <a href="/facts/Chemical_compound/37FXqqtv">compound</a> for treatment of <a href="/facts/Kala_azar/bu6ne799">kala azar</a>) and a new disease, post-kalaazar dermal leishmanoid.'<a class="footnote-ref" id="fnref:136" href="#fn:136">136</a> Brahmachari's cure for Visceral leishmaniasis was the urea salt of para-amino-phenyl stibnic acid which he called Urea Stibamine.<a class="footnote-ref" id="fnref:137" href="#fn:137">137</a> Following the discovery of Urea Stibamine, Visceral leishmaniasis was largely eradicated from the world, except for some underdeveloped regions.<a class="footnote-ref" id="fnref:138" href="#fn:138">138</a></li>
<li><a href="/facts/Ganja/nleMTYJC">Ganja</a> was used as herb for ayurverdic medicine development for last 2,000 years. The Sushruta Samhita, an ancient medical treatise, recommends cannabis plant extract for treating respiratory ailments and diarrhoea.</li>
<li><a href="/facts/Otoplasty/lusLBvNb">Otoplasty</a> – Ear surgery was developed in <a href="/facts/History_of_India/ntYkAYDQ">ancient India</a> and is described in the medical compendium, the <a href="/facts/Sushruta_Samhita/GPSYEjCs">Sushruta Samhita</a> (Sushruta's Compendium, c. 500 AD). The book discussed otoplastic and other <a href="/facts/Plastic_surgery/zLCAX9hN">plastic surgery</a> techniques and procedures for correcting, repairing and reconstructing ears, <a href="/facts/Rhinoplasty/kzd1ll7H">noses</a>, lips, and genitalia that were amputated as criminal, religious, and military punishments. The ancient Indian <a href="/facts/Medicine/2fnp90Je">medical</a> knowledge and plastic surgery techniques of the Sushruta Samhita were practiced throughout Asia until the late 18th century; the October 1794 issue of the contemporary British <a href="/facts/Gentleman%2527s_Magazine/Lf5sWA1n">Gentleman's Magazine</a> reported the practice of <a href="/facts/Rhinoplasty/kzd1ll7H">rhinoplasty</a>, as described in the Sushruta Samhita. Moreover, two centuries later, contemporary practices of otoplastic praxis were derived from the techniques and procedures developed and established in antiquity by Sushruta.<a class="footnote-ref" id="fnref:139" href="#fn:139">139</a><a class="footnote-ref" id="fnref:140" href="#fn:140">140</a></li>
<li><a href="/facts/Tonsillectomy/EmYjyIuI">Tonsillectomy</a> – Tonsillectomies have been practiced for over 2,000 years, with varying popularity over the centuries.<a class="footnote-ref" id="fnref:141" href="#fn:141">141</a> The earliest mention of the procedure is in "Hindu medicine" from about 1000 <a href="/facts/BCE/e5DpqUoe">BCE</a></li>
<li><a href="/facts/Caesarian_section/GJ623ers">Caesarian section</a> – The <a href="/facts/Sanskrit/ychfjhlx">Sanskrit</a> medical treatise <a href="/facts/Sushruta_Samhita/GPSYEjCs">Sushruta Samhita</a>, composed in the early 1st millennium CE, mentions post-mortem caesarean sections.<a class="footnote-ref" id="fnref:142" href="#fn:142">142</a> The first available non-mythical record of a C-section is the mother of <a href="/facts/Bindusara/GBHgYTRG">Bindusara</a> (born c. 320 BC, ruled 298 – c. 272 BC), the second <a href="/facts/Mauryan_empire/STQagR1r">Mauryan</a> Samrat (<a href="/facts/Emperor/qhML5ftb">emperor</a>) of India, accidentally consumed poison and died when she was close to delivering him. <a href="/facts/Chanakya/GPXUmsHn">Chanakya</a>, Chandragupta's teacher and adviser, made up his mind that the baby should survive. He cut open the belly of the queen and took out the baby, thus saving the baby's life.<a class="footnote-ref" id="fnref:143" href="#fn:143">143</a></li></ul>
<h3>Equestrianism</h3>
<ul><li><a href="/facts/Stirrup/pIE4SBNh">Toe stirrup</a> – The earliest known manifestation of the stirrup, which was a toe loop that held the big toe was used in India in as early as 500 BCE<a class="footnote-ref" id="fnref:144" href="#fn:144">144</a> or perhaps by 200 BCE according to other sources.<a class="footnote-ref" id="fnref:145" href="#fn:145">145</a><a class="footnote-ref" id="fnref:146" href="#fn:146">146</a> This ancient stirrup consisted of a looped rope for the big toe which was at the bottom of a saddle made of fibre or leather.<a class="footnote-ref" id="fnref:147" href="#fn:147">147</a> Such a configuration made it suitable for the warm climate of most of India where people used to ride horses barefoot.<a class="footnote-ref" id="fnref:148" href="#fn:148">148</a> A pair of megalithic double bent iron bars with curvature at each end, excavated in <a href="/facts/Stone_circles_of_Junapani/9ffJgyk7">Junapani</a> in the central Indian state of <a href="/facts/Madhya_Pradesh/h8GnUBv6">Madhya Pradesh</a> have been regarded as stirrups although they could as well be something else.<a class="footnote-ref" id="fnref:149" href="#fn:149">149</a> Buddhist carvings in the temples of Sanchi, <a href="/facts/Mathura%2c_Uttar_Pradesh/ShS7I2c5">Mathura</a> and the <a href="/facts/Bhaja_Caves/JMRjh1gE">Bhaja caves</a> dating back between the 1st and 2nd century BCE figure horsemen riding with elaborate saddles with feet slipped under girths.<a class="footnote-ref" id="fnref:150" href="#fn:150">150</a><a class="footnote-ref" id="fnref:151" href="#fn:151">151</a><a class="footnote-ref" id="fnref:152" href="#fn:152">152</a> <a href="/facts/John_Marshall_(archaeologist)/oFCD0eXE">Sir John Marshall</a> described the Sanchi relief as "the earliest example by some five centuries of the use of stirrups in any part of the world".<a class="footnote-ref" id="fnref:153" href="#fn:153">153</a> In the 1st century CE horse riders in northern India, where winters are sometimes long and cold, were recorded to have their booted feet attached to hooked stirrups.<a class="footnote-ref" id="fnref:154" href="#fn:154">154</a> However the form, the conception of the primitive Indian stirrup spread west and east, gradually evolving into the stirrup of today.<a class="footnote-ref" id="fnref:155" href="#fn:155">155</a><a class="footnote-ref" id="fnref:156" href="#fn:156">156</a></li></ul>
<h3>Metallurgy, gems and other commodities</h3>
<ul><li><a href="/facts/History_of_ferrous_metallurgy/XpwtCB0X">Iron working</a> – Iron works were developed in India, around the same time as, but independently of, <a href="/facts/Anatolia/vMkrLrPr">Anatolia</a> and the <a href="/facts/Caucasus/sE8P8Ejg">Caucasus</a>. Archaeological sites in India, such as <a href="/facts/Malhar/djfXJ2Lj">Malhar</a>, Dadupur, Raja Nala Ka Tila and Lahuradewa in present-day <a href="/facts/Uttar_Pradesh/vXDwM9Df">Uttar Pradesh</a> show iron implements in the period between 1800 BCE—1200 BCE.<a class="footnote-ref" id="fnref:157" href="#fn:157">157</a> Early iron objects found in India can be dated to 1400 BCE by employing the method of <a href="/facts/Radiocarbon_dating/qjNglhKP">radiocarbon dating</a>. <a href="/facts/Nail_(fastener)/xjL7LSju">Spikes</a>, <a href="/facts/Knife/6NAX66vY">knives</a>, <a href="/facts/Dagger/bKxEtuKD">daggers</a>, <a href="/facts/Arrow/B21BfJoL">arrow</a>-heads, <a href="/facts/Bowl_(vessel)/jEfbsyws">bowls</a>, <a href="/facts/Spoon/6EvbJtf2">spoons</a>, <a href="/facts/Saucepan/ee6Wtpqd">saucepans</a>, <a href="/facts/Axe/BnaxbVCy">axes</a>, <a href="/facts/Chisel/b3c4f1rH">chisels</a>, tongs, door fittings etc. ranging from 600 BCE to 200 BCE have been discovered from several archaeological sites of India.<a class="footnote-ref" id="fnref:158" href="#fn:158">158</a> Some scholars believe that by the early 13th century BCE, iron smelting was practised on a bigger scale in India, suggesting that the date the technology's inception may be placed earlier.<a class="footnote-ref" id="fnref:159" href="#fn:159">159</a> In <a href="/facts/Southern_India/XqkE3NdU">Southern India</a> (present day <a href="/facts/Mysore/xpzbccId">Mysore</a>) iron appeared as early as 11th to 12th centuries BCE; these developments were too early for any significant close contact with the northwest of the country.<a class="footnote-ref" id="fnref:160" href="#fn:160">160</a> In the time of <a href="/facts/Chandragupta_II/7rVuJoIn">Chandragupta II</a> Vikramaditya (375–413 CE), corrosion-resistant iron was used to erect the <a href="/facts/Iron_pillar_of_Delhi/fEkgaNVE">Iron pillar of Delhi</a>, which has withstood corrosion for over 1,600 years.<a class="footnote-ref" id="fnref:161" href="#fn:161">161</a></li>
<li><a href="/facts/Crucible_steel/ThwscHH3">Crucible steel</a> – Perhaps as early as 300 BCE—although certainly by 200 BCE—high quality steel was being produced in southern India, by what Europeans would later call the crucible technique.<a class="footnote-ref" id="fnref:162" href="#fn:162">162</a> In this system, high-purity wrought iron, charcoal, and glass were mixed in a crucible and heated until the iron melted and absorbed the carbon.<a class="footnote-ref" id="fnref:163" href="#fn:163">163</a></li>
<li><a href="/facts/Dockyard/hxUHLNN6">Dockyard</a> – The world's earliest enclosed dockyard was built in the Harappan port city of <a href="/facts/Lothal/hdAJu6Uf">Lothal</a> circa 2600 BC in Gujarat, India.<a class="footnote-ref" id="fnref:164" href="#fn:164">164</a><a class="footnote-ref" id="fnref:165" href="#fn:165">165</a></li>
<li><a href="/facts/Diamond_cut/kXpYezW4">Diamond drills</a> – in the 12th century BCE or 7th century BCE, Indians not only innovated use of diamond tipped drills but also invented double diamond tipped drills for bead manufacturing.<a class="footnote-ref" id="fnref:166" href="#fn:166">166</a></li>
<li><a href="/facts/Diamond_cut/kXpYezW4">Diamond cutting and polishing</a> – The technology of cutting and polishing diamonds was invented in India, Ratnapariksha, a text dated to 6th century talks about diamond cutting and Al-Beruni speaks about the method of using lead plate for diamond polishing in the 11th century CE.<a class="footnote-ref" id="fnref:167" href="#fn:167">167</a></li>
<li><a href="/facts/Draw_bar/h9hklhto">Draw bar</a> – The draw bar was applied to sugar-milling, with evidence of its use at <a href="/facts/Delhi/Xa6CKgnf">Delhi</a> in the <a href="/facts/Mughal_Empire/yRg2kAy5">Mughal Empire</a> by 1540, but possibly dating back several centuries earlier to the <a href="/facts/Delhi_Sultanate/19oLzpBF">Delhi Sultanate</a>.<a class="footnote-ref" id="fnref:168" href="#fn:168">168</a></li>
<li><a href="/facts/Etched_carnelian_beads/BxIDQ3ye">Etched carnelian beads</a> – are a type of ancient decorative beads made from <a href="/facts/Carnelian/knKJs122">carnelian</a> with an etched design in white. They were made according to a technique of alkaline-etching developed by the <a href="/facts/Harappa/bKWEUjH0">Harappans during the 3rd millennium BCE</a> and were widely disperced from China in the east to Greece in the west.<a class="footnote-ref" id="fnref:169" href="#fn:169">169</a><a class="footnote-ref" id="fnref:170" href="#fn:170">170</a><a class="footnote-ref" id="fnref:171" href="#fn:171">171</a></li>
<li><a href="/facts/Glassblowing/dWf2rYAD">Glassblowing</a> – Rudimentary form of glass blowing from <a href="/facts/Indian_subcontinent/0XUWGXpx">Indian subcontinent</a> is attested earlier than Western Asian counterparts(where it is attested not earlier than 1st century BCE) in the form of <a href="/facts/Indo-Pacific_beads/KTlgI5g2">Indo-Pacific beads</a> which uses glass blowing to make cavity before being subjected to <a href="/facts/Tube_drawing/cwKTsyzI">tube drawn technique</a> for bead making dated more than 2500 BP.<a class="footnote-ref" id="fnref:172" href="#fn:172">172</a><a class="footnote-ref" id="fnref:173" href="#fn:173">173</a> Beads are made by attaching molten glass gather to the end of a blowpipe, a bubble is then blown into the gather.<a class="footnote-ref" id="fnref:174" href="#fn:174">174</a> The glass blown vessels were rarely attested and were imported commodity in 1st millennium CE though.</li>
<li><a href="/facts/Lost-wax_casting/XBJhX40E">Lost-wax casting</a> – Metal casting by the <a href="/facts/Indus_Valley_civilization/6xM4aK23">Indus Valley civilization</a> began around 3500 BC in the <a href="/facts/Mohenjodaro/aC8lQMa4">Mohenjodaro</a> area,<a class="footnote-ref" id="fnref:175" href="#fn:175">175</a> which produced one of the earliest known examples of lost-wax casting, an Indian bronze figurine named the "<a href="/facts/Dancing_Girl_(prehistoric_sculpture)/NRaKUxjQ">dancing girl</a>" that dates back nearly 5,000 years to the <a href="/facts/Indus_Valley_civilization/6xM4aK23">Harappan</a> period (c. 3300–1300 BC).<a class="footnote-ref" id="fnref:176" href="#fn:176">176</a><a class="footnote-ref" id="fnref:177" href="#fn:177">177</a> Other examples include the buffalo, bull and dog found at Mohenjodaro and <a href="/facts/Harappa/bKWEUjH0">Harappa</a>,<a class="footnote-ref" id="fnref:178" href="#fn:178">178</a><a class="footnote-ref" id="fnref:179" href="#fn:179">179</a><a class="footnote-ref" id="fnref:180" href="#fn:180">180</a> two <a href="/facts/Copper/I8PEE8oX">copper</a> figures found at the Harappan site <a href="/facts/Lothal/hdAJu6Uf">Lothal</a> in the district of Ahmedabad of Gujarat,<a class="footnote-ref" id="fnref:181" href="#fn:181">181</a> and likely a covered cart with wheels missing and a complete cart with a driver found at <a href="/facts/Chanhudaro/p4jPdJs5">Chanhudaro</a>.<a class="footnote-ref" id="fnref:182" href="#fn:182">182</a><a class="footnote-ref" id="fnref:183" href="#fn:183">183</a></li>
<li>Seamless <a href="/facts/Celestial_globe/wggopTWc">celestial globe</a> – Considered one of the most remarkable feats in <a href="/facts/Metallurgy/1SANyxX4">metallurgy</a>, it was invented in India in between 1589 and 1590 CE.<a class="footnote-ref" id="fnref:184" href="#fn:184">184</a><a class="footnote-ref" id="fnref:185" href="#fn:185">185</a> Before they were rediscovered in the 1980s, it was believed by modern metallurgists to be technically impossible to produce metal globes without any seams, even with modern technology.<a class="footnote-ref" id="fnref:186" href="#fn:186">186</a></li>
<li><a href="/facts/Stoneware/h6JS15YF">Stoneware</a> – Earliest stonewares, predecessors of <a href="/facts/Porcelain/deuLm3sb">porcelain</a> have been recorded at Indus Valley Civilization sites of <a href="/facts/Harappa/bKWEUjH0">Harappa</a> and <a href="/facts/Mohenjo-daro/aC8lQMa4">Mohenjo Daro</a>, they were used for making stoneware bangles.<a class="footnote-ref" id="fnref:187" href="#fn:187">187</a><a class="footnote-ref" id="fnref:188" href="#fn:188">188</a><a class="footnote-ref" id="fnref:189" href="#fn:189">189</a></li>
<li><a href="/facts/Tube_drawing/cwKTsyzI">Tube drawn</a> technology: Indians used tube drawn technology for glass bead manufacturing which was first developed in the 2nd century BCE.<a class="footnote-ref" id="fnref:190" href="#fn:190">190</a><a class="footnote-ref" id="fnref:191" href="#fn:191">191</a><a class="footnote-ref" id="fnref:192" href="#fn:192">192</a></li>
<li><a href="/facts/Tumble_finishing/3yM698Ee">Tumble polishing</a> – Indians innvoted polishing method in the 10th century BCE for mass production of polished stone beads.<a class="footnote-ref" id="fnref:193" href="#fn:193">193</a><a class="footnote-ref" id="fnref:194" href="#fn:194">194</a><a class="footnote-ref" id="fnref:195" href="#fn:195">195</a><a class="footnote-ref" id="fnref:196" href="#fn:196">196</a></li>
<li><a href="/facts/Wootz_steel/vVsqg46c">Wootz steel</a> – Wootz steel is an ultra-high carbon steel and the first form of crucible steel manufactured by the applications and use of <a href="/facts/Nanomaterials/BthrFILJ">nanomaterials</a> in its microstructure and is characterised by its ultra-high carbon content exhibiting properties such as superplasticity and high impact hardness.<a class="footnote-ref" id="fnref:197" href="#fn:197">197</a> Archaeological and <a href="/facts/Tamil_language/7I0lHL0d">Tamil language</a> <a href="/facts/Sangam_literature/xQaCAxcM">literary</a> evidence suggests that this manufacturing process was already in existence in South India well before the common era, with <a href="/facts/Wootz_steel/vVsqg46c">wootz steel</a> exported from the <a href="/facts/Chera/uRDQy2wX">Chera</a> dynasty and called Seric Iron in Rome, and later known as <a href="/facts/Damascus_steel/KVEnGTGB">Damascus steel</a> in Europe.<a class="footnote-ref" id="fnref:198" href="#fn:198">198</a><a class="footnote-ref" id="fnref:199" href="#fn:199">199</a><a class="footnote-ref" id="fnref:200" href="#fn:200">200</a><a class="footnote-ref" id="fnref:201" href="#fn:201">201</a> Reproduction research is undertaken by scientists Dr. Oleg Sherby and Dr. Jeff Wadsworth and the <a href="/facts/Lawrence_Livermore_National_Laboratory/WuXIbIKz">Lawrence Livermore National Laboratory</a> have all attempted to create steels with characteristics similar to Wootz, but without success. J.D Verhoeven and Al Pendray attained some success in the reconstruction methods of production, proved the role of impurities of ore in the pattern creation, and reproduced Wootz steel with patterns microscopically and visually identical to one of the ancient blade patterns.<a class="footnote-ref" id="fnref:202" href="#fn:202">202</a></li>
<li><a href="/facts/Rain_gauge/vuGawrhQ">Rain gauge</a> – People living in <a href="/facts/India/QW4TV4sy">India</a> began to record rainfall in 400 BCE.<a class="footnote-ref" id="fnref:203" href="#fn:203">203</a> The readings were correlated against expected growth. In the <a href="/facts/Arthashastra/Sm0NRGrW">Arthashastra</a>, used for example in <a href="/facts/Magadha_(Mahajanapada)/e2vLVE9U">Magadha</a>, precise standards were set as to grain production. Each state storehouse was equipped with a rain gauge to classify land for taxation purposes.<a class="footnote-ref" id="fnref:204" href="#fn:204">204</a></li>
<li><a href="/facts/Touchstone_(assaying_tool)/f0tPARCM">Touchstone</a> – The touchstone was used during the <a href="/facts/Indus_Valley_civilization/6xM4aK23">Harappa period of the Indus Valley civilization</a> ca. 2600–1900 BC for testing the purity of soft metals.<a class="footnote-ref" id="fnref:205" href="#fn:205">205</a></li></ul>
<h3>Metrology</h3>
<ul><li><a href="/facts/Standardisation/vS9AhNMS">Standardisation</a> – The oldest applications and evidence of standardisation come from the Indus Valley Civilisation in the 5th millennium BCE characterised by the existence of weights in various standards and categories as<a class="footnote-ref" id="fnref:206" href="#fn:206">206</a> well as the Indus merchants usage of a centralised weight and measure system. Small weights were used to measure luxury goods, and larger weights were used for buying bulkier items, such as food grains etc.<a class="footnote-ref" id="fnref:207" href="#fn:207">207</a> The weights and measures of the Indus civilisation also reached <a href="/facts/Persia/24yukge8">Persia</a> and <a href="/facts/Central_Asia/rB8k0CyT">Central Asia</a>, where they were further modified.<a class="footnote-ref" id="fnref:208" href="#fn:208">208</a></li></ul>
 <blockquote> A total of 558 weights were excavated from Mohenjodaro, Harappa, and <a href="/facts/Chanhudaro/p4jPdJs5">Chanhu-daro</a>, not including defective weights. They did not find statistically significant differences between weights that were excavated from five different layers, each about 1.5 m in thickness. This was evidence that strong control existed for at least a 500-year period. The 13.7-g weight seems to be one of the units used in the Indus valley. The notation was based on the <a href="/facts/Binary_numeral_system/a6JDSRPs">binary</a> and <a href="/facts/Decimal/7omfVNIM">decimal</a> systems. 83% of the weights which were excavated from the above three cities were cubic, and 68% were made of <a href="/facts/Chert/pmvbVy6U">chert</a>.<a class="footnote-ref" id="fnref:209" href="#fn:209">209</a> </blockquote>
<ul><li><a href="/facts/Technical_standards/P4orT1SM">Technical standards</a> – Technical standards were being applied and used in the <a href="/facts/Indus_Valley_civilisation/6xM4aK23">Indus Valley civilisation</a> since the 5th millennium BCE to enable gauging devices to be effectively used in <a href="/facts/Angular_measurement/gFUTEQYq">angular measurement</a> and <a href="/facts/Measurement/rsLLbn1s">measurement</a> in construction.<a class="footnote-ref" id="fnref:210" href="#fn:210">210</a> Uniform units of length were used in the planning and construction of towns such as <a href="/facts/Lothal/hdAJu6Uf">Lothal</a>, <a href="/facts/Surkotada/DM8EtgPs">Surkotada</a>, <a href="/facts/Kalibangan/S6HT1GqR">Kalibangan</a>, <a href="/facts/Dholavira/APzMFAPQ">Dholavira</a>, <a href="/facts/Harappa/bKWEUjH0">Harappa</a>, and <a href="/facts/Mohenjo-daro/aC8lQMa4">Mohenjo-daro</a>.<a class="footnote-ref" id="fnref:211" href="#fn:211">211</a> The weights and measures of the Indus civilisation also reached <a href="/facts/Persia/24yukge8">Persia</a> and <a href="/facts/Central_Asia/rB8k0CyT">Central Asia</a>, where they were further modified.<a class="footnote-ref" id="fnref:212" href="#fn:212">212</a></li></ul>
<h3>Weapons</h3>
<ul><li>Metal cylinder <a href="/facts/Rocket/b6j4keIl">rocket</a>: In the 16th century, <a href="/facts/Akbar/e92T534P">Akbar</a> was the first to initiate and use metal cylinder rockets known as bans, particularly against <a href="/facts/War_elephant/Wk06pvpv">war elephants</a>, during the Battle of Sanbal.<a class="footnote-ref" id="fnref:213" href="#fn:213">213</a>[better source needed]</li>
<li><a href="/facts/Mysorean_rockets/1cs69vCw">Mysorean rockets</a> – One of the first iron-cased <a href="/facts/Rocket/b6j4keIl">rockets</a> were deployed by <a href="/facts/Hyder_Ali/MJdrt4jX">Hyder Ali</a>'s army, ruler of the South Indian <a href="/facts/Kingdom_of_Mysore/7Yeur3m4">Kingdom of Mysore</a>.<a class="footnote-ref" id="fnref:214" href="#fn:214">214</a></li>
<li><a href="/facts/Rocket_artillery/pJ9RehcA">Rocket artillery</a> - The first true rocket artillery was developed by <a href="/facts/Tipu_Sultan/U7y0Qtfe">Tipu Sultan</a> and was notably in use during the <a href="/facts/Anglo-Mysore_Wars/9tC8BEI5">Anglo-Mysore Wars</a>.<a class="footnote-ref" id="fnref:215" href="#fn:215">215</a><a class="footnote-ref" id="fnref:216" href="#fn:216">216</a></li></ul>
<h3>Philosophy and logic</h3>
<ul><li><a href="/facts/Catu%25E1%25B9%25A3ko%25E1%25B9%25ADi/tBu6q2yw">Catuskoti (Tetralemma)</a> – The four-cornered system of logical argumentation with a suite of four distinct functions that refers to a logical proposition P, with four possibilities that can arise. The tetralemma has many <a href="/facts/Epistemology/NsDwpcYH">logico-epistemological</a> applications and has been made ample use of by the Indian philosopher <a href="/facts/Nagarjuna/PQTPm3y2">Nāgarjuna</a> in the <a href="/facts/Madhyamaka/l9cTXysP">Madhyamaka</a> school. The tetralemma also features prominently in the Greek <a href="/facts/Skepticism/qXAgbbVT">skepticist</a> school of <a href="/facts/Pyrrhonism/sNany6Qc">Pyrrhonism</a>, the teachings of which are based on Buddhism. According to <a href="/facts/Christopher_I._Beckwith/EtTzlFXW">Christopher I. Beckwith</a> ,the founder of the Pyrrhonist school lived in India for 18 months and likely learned the language, which allowed him to carry these teachings to Greece.<a class="footnote-ref" id="fnref:217" href="#fn:217">217</a> However, other scholars, such as <a href="/facts/Stephen_Batchelor_(author)/RINDsKpt">Stephen Batchelor</a><a class="footnote-ref" id="fnref:218" href="#fn:218">218</a> and Charles Goodman<a class="footnote-ref" id="fnref:219" href="#fn:219">219</a> question Beckwith's conclusions about the degree of Buddhist influence on Pyrrho</li>
<li><a href="/facts/Trair%25C5%25ABpya/LzEbk6XF">Trairūpya</a> – Trairūpya is a logical argument that contains three constituents which a logical ‘sign’ or ‘mark’ (linga) must fulfill to be 'valid source of knowledge' (<a href="/facts/Pramana/ay65BFp3">pramana</a>):</li></ul>
<ol><li>It should be present in the case or object under consideration, the ‘subject-locus' (pakṣa)</li>
<li>It should be present in a ‘similar case’ or a homologue (sapakṣa)</li>
<li>It should not be present in any ‘dissimilar case’ or heterologue (vipakṣa)</li></ol>
When a ‘sign’ or ‘mark’ (linga) is identified, there are three possibilities: the sign may be present in all, some, or none of the sapakṣas. Likewise, the sign may be present in all, some or none of the vipakṣas. To identify a sign, we have to assume that it is present in the pakṣa, however; that is the first condition is already satisfied. Combining these, Dignaga constructed his ‘Wheel of Reason’ (Sanskrit: <a href="/facts/Hetucakra/E6w7WzLm">Hetucakra</a>).<a class="footnote-ref" id="fnref:220" href="#fn:220">220</a>
<ul><li><a href="/facts/Jaina_seven-valued_logic/CggXhoNT">Jaina seven-valued logic</a> – The Saptabhangivada, the seven predicate theory may be summarized as follows:<a class="footnote-ref" id="fnref:221" href="#fn:221">221</a></li></ul>
The seven predicate theory consists in the use of seven claims about sentences, each preceded by "arguably" or "conditionally" (syat), concerning a single object and its particular properties, composed of assertions and denials, either simultaneously or successively, and without contradiction. These seven claims are the following.
<ol><li>Arguably, it (that is, some object) exists (syad asty eva).</li>
<li>Arguably, it does not exist (syan nasty eva).</li>
<li>Arguably, it exists; arguably, it doesn't exist (syad asty eva syan nasty eva).</li>
<li>Arguably, it is non-assertible (syad avaktavyam eva).</li>
<li>Arguably, it exists; arguably, it is non-assertible (syad asty eva syad avaktavyam eva).</li>
<li>Arguably, it doesn't exist; arguably, it is non-assertible (syan nasty eva syad avaktavyam eva).</li>
<li>Arguably, it exists; arguably, it doesn't exist; arguably it is non-assertible (syad asty eva syan nasty eva syad avaktavyam eva).</li></ol>
<h3>Mathematics</h3>
See also: <a href="/facts/Indian_mathematics/l9f6ke00">Indian mathematics</a>
<table><tbody><tr><th rowspan="2">Number System</th><th colspan="10">Numbers</th></tr><tr><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th></tr><tr><th>Tamil</th><td>೦</td><td>௧</td><td>௨</td><td>௩</td><td>௪</td><td>௫</td><td>௬</td><td>௭</td><td>௮</td><td>௯</td></tr><tr><th>Gurmukhi</th><td>o</td><td>੧</td><td>੨</td><td>੩</td><td>੪</td><td>੫</td><td>੬</td><td>੭</td><td>੮</td><td>੯</td></tr><tr><th>Odia</th><td>୦</td><td>୧</td><td>୨</td><td>୩</td><td>୪</td><td>୫</td><td>୬</td><td>୭</td><td>୮</td><td>୯</td></tr><tr><th>Bengali</th><td>০</td><td>১</td><td>২</td><td>৩</td><td>৪</td><td>৫</td><td>৬</td><td>৭</td><td>৮</td><td>৯</td></tr><tr><th>Assamese</th><td>০</td><td>১</td><td>২</td><td>৩</td><td>৪</td><td>৫</td><td>৬</td><td>৭</td><td>৮</td><td>৯</td></tr><tr><th>Devanagari</th><td>०</td><td>१</td><td>२</td><td>३</td><td>४</td><td>५</td><td>६</td><td>७</td><td>८</td><td>९</td></tr><tr><th>Gujarati</th><td>૦</td><td>૧</td><td>૨</td><td>૩</td><td>૪</td><td>૫</td><td>૬</td><td>૭</td><td>૮</td><td>૯</td></tr><tr><th>Tibetan</th><td>༠</td><td>༡</td><td>༢</td><td>༣</td><td>༤</td><td>༥</td><td>༦</td><td>༧</td><td>༨</td><td>༩</td></tr><tr><th>Telugu</th><td>౦</td><td>౧</td><td>౨</td><td>౩</td><td>౪</td><td>౫</td><td>౬</td><td>౭</td><td>౮</td><td>౯</td></tr><tr><th>Kannada</th><td>೦</td><td>೧</td><td>೨</td><td>೩</td><td>೪</td><td>೫</td><td>೬</td><td>೭</td><td>೮</td><td>೯</td></tr><tr><th>Malayalam</th><td>൦</td><td>൧</td><td>൨</td><td>൩</td><td>൪</td><td>൫</td><td>൬</td><td>൭</td><td>൮</td><td>൯</td></tr><tr><th>Burmese</th><td>၀</td><td>၁</td><td>၂</td><td>၃</td><td>၄</td><td>၅</td><td>၆</td><td>၇</td><td>၈</td><td>၉</td></tr><tr><th>Khmer</th><td>០</td><td>១</td><td>២</td><td>៣</td><td>៤</td><td>៥</td><td>៦</td><td>៧</td><td>៨</td><td>៩</td></tr><tr><th>Thai</th><td>๐</td><td>๑</td><td>๒</td><td>๓</td><td>๔</td><td>๕</td><td>๖</td><td>๗</td><td>๘</td><td>๙</td></tr><tr><th>Lao</th><td>໐</td><td>໑</td><td>໒</td><td>໓</td><td>໔</td><td>໕</td><td>໖</td><td>໗</td><td>໘</td><td>໙</td></tr><tr><th>Balinese</th><td>᭐</td><td>᭑</td><td>᭒</td><td>᭓</td><td>᭔</td><td>᭕</td><td>᭖</td><td>᭗</td><td>᭘</td><td>᭙</td></tr><tr><th>Santali</th><td>᱐</td><td>᱑</td><td>᱒</td><td>᱓</td><td>᱔</td><td>᱕</td><td>᱖</td><td>᱗</td><td>᱘</td><td>᱙</td></tr><tr><th>Javanese</th><td>꧐</td><td>꧑</td><td>꧒</td><td>꧓</td><td>꧔</td><td>꧕</td><td>꧖</td><td>꧗</td><td>꧘</td><td>꧙</td></tr></tbody></table>

<ul><li><a href="/facts/0_(number)/4NBRtKHc">Zero</a> – Zero and its operation are first defined by (Hindu astronomer and mathematician) Brahmagupta in 628.<a class="footnote-ref" id="fnref:222" href="#fn:222">222</a> The Babylonians used a space, and later a zero glyph, in their written <a href="/facts/Sexagesimal/bspNRWdR">Sexagesimal</a> system, to signify the 'absent',<a class="footnote-ref" id="fnref:223" href="#fn:223">223</a> the Olmecs used a positional zero glyph in their <a href="/facts/Vigesimal/zvzFVBsL">Vigesimal</a> system, the Greeks, from <a href="/facts/Ptolemy/htudGQTQ">Ptolemy</a>'s <a href="/facts/Almagest/30qaBRAq">Almagest</a>, in a <a href="/facts/Sexagesimal/bspNRWdR">Sexagesimal</a> system. The Chinese used a blank, in the written form of their decimal <a href="/facts/Counting_rods/lg4P6zoG">Counting rods</a> system. A dot, rather than a blank, was first seen to denote zero, in a decimal system, in the <a href="/facts/Bakhshali_manuscript/5Xb27h7v">Bakhshali manuscript</a>.<a class="footnote-ref" id="fnref:224" href="#fn:224">224</a> The usage of the zero in the Bakhshali manuscript was dated from between 3rd and 4th centuries, making it the earliest known usage of a written zero, in a decimal place value system.<a class="footnote-ref" id="fnref:225" href="#fn:225">225</a></li>
<li><a href="/facts/Hindu%25E2%2580%2593Arabic_numeral_system/z73KvotW">Hindu number system</a> – With <a href="/facts/Decimal/7omfVNIM">decimal</a> place-value and a symbol for zero, this system was the ancestor of the widely used <a href="/facts/Arabic_numeral/LryNhh26">Arabic numeral</a> system. It was developed in the Indian subcontinent between the 1st and 6th centuries CE.<a class="footnote-ref" id="fnref:226" href="#fn:226">226</a><a class="footnote-ref" id="fnref:227" href="#fn:227">227</a></li>
<li>Law of signs in multiplication – The earliest use of notation for negative numbers, as <a href="/facts/Subtrahend/dEUrp6k0">subtrahend</a>, is credited by scholars to the Chinese, dating back to the 2nd century BCE.<a class="footnote-ref" id="fnref:228" href="#fn:228">228</a> Like the Chinese, the Indians used negative numbers as subtrahend, but were the first to establish the "law of signs" with regards to the multiplication of positive and negative numbers, which did not appear in Chinese texts until 1299.<a class="footnote-ref" id="fnref:229" href="#fn:229">229</a> Indian mathematicians were aware of negative numbers by the 7th century,<a class="footnote-ref" id="fnref:230" href="#fn:230">230</a> and their role in mathematical problems of debt was understood.<a class="footnote-ref" id="fnref:231" href="#fn:231">231</a> Mostly consistent and correct rules for working with negative numbers were formulated,<a class="footnote-ref" id="fnref:232" href="#fn:232">232</a> and the diffusion of these rules led the Arab intermediaries to pass it on to Europe.,<a class="footnote-ref" id="fnref:233" href="#fn:233">233</a> for example (+)×(-)=(-),(-)×(-)=(+) etc.</li>
<li><a href="/facts/Sign_convention/0yGl2bzD">Sign convention</a> – Symbols, signs and mathematical notation were employed in an early form in India by the 6th century when the mathematician-astronomer Aryabhata recommended the use of letters to represent unknown quantities.<a class="footnote-ref" id="fnref:234" href="#fn:234">234</a> By the 7th century Brahmagupta had already begun using abbreviations for unknowns, even for multiple unknowns occurring in one complex problem.<a class="footnote-ref" id="fnref:235" href="#fn:235">235</a> Brahmagupta also managed to use abbreviations for square roots and cube roots.<a class="footnote-ref" id="fnref:236" href="#fn:236">236</a> By the 7th century fractions were written in a manner similar to the modern times, except for the bar separating the <a href="/facts/Numerator/ghnQE9B3">numerator</a> and the <a href="/facts/Denominator/ghnQE9B3">denominator</a>.<a class="footnote-ref" id="fnref:237" href="#fn:237">237</a> A dot symbol for <a href="/facts/Negative_numbers/LzErzCmI">negative numbers</a> was also employed.<a class="footnote-ref" id="fnref:238" href="#fn:238">238</a> The <a href="/facts/Bakhshali_Manuscript/5Xb27h7v">Bakhshali Manuscript</a> displays a cross, much like the modern '+' sign, except that it symbolised subtraction when written just after the number affected.<a class="footnote-ref" id="fnref:239" href="#fn:239">239</a> The '=' sign for equality did not exist.<a class="footnote-ref" id="fnref:240" href="#fn:240">240</a> Indian mathematics was transmitted to the Islamic world where this notation was seldom accepted initially and the scribes continued to write mathematics in full and without symbols.<a class="footnote-ref" id="fnref:241" href="#fn:241">241</a></li>
<li>Modern <a href="/facts/Elementary_arithmetic/aUn5tGtp">elementary arithmetic</a> – Modum indorum or the method of the Indians for arithmetic operations was popularised by Al-Khwarizmi and Al-Kindi by means of their respective works such as in Al-Khwarizmi's on the Calculation with Hindu Numerals (ca. 825), On the Use of the Indian Numerals (ca. 830)<a class="footnote-ref" id="fnref:242" href="#fn:242">242</a> as early as the 8th and 9th centuries.They, amongst other works, contributed to the diffusion of the Indian system of arithmetic in the Middle-East and the West.The significance of the development of the positional number system is described by the French mathematician Pierre Simon Laplace (1749–1827) who wrote:</li></ul>
<blockquote>"It is India that gave us the ingenuous method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity."</blockquote>
<ul><li><a href="/facts/Chakravala_method/aEsVHc7s">Chakravala method</a> – The Chakravala method, a cyclic algorithm to solve <a href="/facts/Indeterminate_equation/DwdC3hyK">indeterminate</a> <a href="/facts/Quadratic_equation/9IMnkJAT">quadratic equations</a> is commonly attributed to <a href="/facts/Bh%25C4%2581skara_II/BQlUY9gA">Bhāskara II</a>, (c. 1114 – 1185 CE)<a class="footnote-ref" id="fnref:243" href="#fn:243">243</a><a class="footnote-ref" id="fnref:244" href="#fn:244">244</a><a class="footnote-ref" id="fnref:245" href="#fn:245">245</a> although some attribute it to <a href="/facts/Jayadeva_(mathematician)/2IvWoJtY">Jayadeva</a> (c. 950~1000 CE).<a class="footnote-ref" id="fnref:246" href="#fn:246">246</a> Jayadeva pointed out that Brahmagupta's approach to solving equations of this type would yield infinitely large number of solutions, to which he then described a general method of solving such equations.<a class="footnote-ref" id="fnref:247" href="#fn:247">247</a> Jayadeva's method was later refined by Bhāskara II in his <a href="/facts/Bijaganita/wr7jaubX">Bijaganita</a> treatise to be known as the Chakravala method, <a href="/facts/Chakra/eD8fRyqH">chakra</a> (derived from cakraṃ चक्रं) meaning 'wheel' in <a href="/facts/Sanskrit/ychfjhlx">Sanskrit</a>, relevant to the cyclic nature of the algorithm.<a class="footnote-ref" id="fnref:248" href="#fn:248">248</a><a class="footnote-ref" id="fnref:249" href="#fn:249">249</a> With reference to the Chakravala method, E. O. Selenuis held that no European performances at the time of Bhāskara, nor much later, came up to its marvellous height of mathematical complexity.<a class="footnote-ref" id="fnref:250" href="#fn:250">250</a><a class="footnote-ref" id="fnref:251" href="#fn:251">251</a><a class="footnote-ref" id="fnref:252" href="#fn:252">252</a></li>
<li><a href="/facts/Trigonometric_function/czej7ur0">Trigonometric functions</a> – The <a href="/facts/Trigonometry/K4hfaC6F">trigonometric</a> functions sine and versine originated in <a href="/facts/Indian_astronomy/q9pgvuCm">Indian astronomy</a> along with the cosine and inversine , adapted from the full-chord Greek versions (to the modern half-chord versions). They were described in detail by <a href="/facts/Aryabhata/3L1j5TDm">Aryabhata</a> in the late 5th century, but were likely developed earlier in the <a href="/facts/Pancha-Siddhantika/zgAxCKuR">Siddhantas</a>, astronomical treatises of the 3rd or 4th century.<a class="footnote-ref" id="fnref:253" href="#fn:253">253</a><a class="footnote-ref" id="fnref:254" href="#fn:254">254</a> Later, the 6th-century astronomer <a href="/facts/Varahamihira/zgAxCKuR">Varahamihira</a> discovered a few basic trigonometric formulas and identities, such as sin^2(x) + cos^2(x) = 1.<a class="footnote-ref" id="fnref:255" href="#fn:255">255</a></li>
<li><a href="/facts/Mean_value_theorem/JnjkzQb4">Mean value theorem</a> – A special case of this <a href="/facts/Theorem/f2Pe1FMD">theorem</a> for inverse interpolation of the sine was first described by <a href="/facts/Parameshvara/AWouaecc">Parameshvara</a> (1380–1460), from the <a href="/facts/Kerala_School_of_Astronomy_and_Mathematics/lkJPFMKe">Kerala School of Astronomy and Mathematics</a> in <a href="/facts/India/QW4TV4sy">India</a>, in his commentaries on <a href="/facts/Govindasv%25C4%2581mi/AcYgFAa8">Govindasvāmi</a> and <a href="/facts/Bh%25C4%2581skara_II/BQlUY9gA">Bhāskara II</a>.<a class="footnote-ref" id="fnref:256" href="#fn:256">256</a></li>
<li><a href="/facts/Bh%25C4%2581skara_I%2527s_sine_approximation_formula/4Br4KU52">Bhāskara I's sine approximation formula</a></li>
<li><a href="/facts/Madhava_series/Vng3X9s1">Madhava series</a> – The infinite series for π and for the trigonometric <a href="/facts/Sine/gQ6LXK8z">sine</a>, <a href="/facts/Cosine/czej7ur0">cosine</a>, and <a href="/facts/Arctangent/bVwU9FPG">arctangent</a> is now attributed to Madhava of Sangamagrama (c. 1340 – 1425) and his Kerala school of astronomy and mathematics.<a class="footnote-ref" id="fnref:257" href="#fn:257">257</a><a class="footnote-ref" id="fnref:258" href="#fn:258">258</a> He made use of the series expansion of 
 
 
 
 arctan
 ⁡
 x
 
 
 {\displaystyle \arctan x}
 
 to obtain an infinite series expression for π.<a class="footnote-ref" id="fnref:259" href="#fn:259">259</a> Their rational approximation of the error for the finite sum of their series are of particular interest. They manipulated the error term to derive a faster converging series for π.<a class="footnote-ref" id="fnref:260" href="#fn:260">260</a> They used the improved series to derive a rational expression,<a class="footnote-ref" id="fnref:261" href="#fn:261">261</a>
 
 
 
 104348
 
 /
 
 33215
 
 
 {\displaystyle 104348/33215}
 
 for π correct up to eleven decimal places, i.e. 
 
 
 
 3.1415926539214
 
 
 {\displaystyle 3.1415926539214}
 
.<a class="footnote-ref" id="fnref:262" href="#fn:262">262</a><a class="footnote-ref" id="fnref:263" href="#fn:263">263</a> Madhava of Sangamagrama and his successors at the <a href="/facts/Kerala_school_of_astronomy_and_mathematics/lkJPFMKe">Kerala school of astronomy and mathematics</a> used geometric methods to derive large sum approximations for sine, cosine, and arctangent. They found a number of special cases of series later derived by Brook Taylor series. They also found the second-order Taylor approximations for these functions, and the third-order Taylor approximation for sine.<a class="footnote-ref" id="fnref:264" href="#fn:264">264</a><a class="footnote-ref" id="fnref:265" href="#fn:265">265</a><a class="footnote-ref" id="fnref:266" href="#fn:266">266</a></li>
<li><a href="/facts/Power_series/vYh6sTps">Power series</a> – The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India. Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation and integration.<a class="footnote-ref" id="fnref:267" href="#fn:267">267</a></li>
<li>Finite difference <a href="/facts/Interpolation/8PyetX4f">interpolation</a> – The Indian mathematician <a href="/facts/Brahmagupta/f7uxKXo4">Brahmagupta</a> presented what is possibly the first instance<a class="footnote-ref" id="fnref:268" href="#fn:268">268</a><a class="footnote-ref" id="fnref:269" href="#fn:269">269</a> of finite difference interpolation around 665 CE.<a class="footnote-ref" id="fnref:270" href="#fn:270">270</a></li>
<li><a href="/facts/Algebra/nMdqczjo">Algebraic abbreviations</a> – The mathematician <a href="/facts/Brahmagupta/f7uxKXo4">Brahmagupta</a> had begun using abbreviations for unknowns by the 7th century.<a class="footnote-ref" id="fnref:271" href="#fn:271">271</a> He employed abbreviations for multiple unknowns occurring in one complex problem.<a class="footnote-ref" id="fnref:272" href="#fn:272">272</a> Brahmagupta also used abbreviations for <a href="/facts/Square_roots/AfrzfBdQ">square roots</a> and <a href="/facts/Cube_roots/c8klHLFb">cube roots</a>.<a class="footnote-ref" id="fnref:273" href="#fn:273">273</a></li>
<li><a href="/facts/Permutation/JSw9ukmv">Systematic generation of all permutations</a> – The method goes back to <a href="/facts/Narayana_Pandit/p9u2tV57">Narayana Pandita</a> in 14th century India, and has been rediscovered frequently.<a class="footnote-ref" id="fnref:274" href="#fn:274">274</a></li>
<li>Discovered by the Indian mathematician, Brahmagupta (598–668 CE):<a class="footnote-ref" id="fnref:275" href="#fn:275">275</a><a class="footnote-ref" id="fnref:276" href="#fn:276">276</a><a class="footnote-ref" id="fnref:277" href="#fn:277">277</a><a class="footnote-ref" id="fnref:278" href="#fn:278">278</a>
<ul><li><a href="/facts/Brahmagupta%25E2%2580%2593Fibonacci_identity/brCDr0Rn">Brahmagupta–Fibonacci identity</a></li>
<li><a href="/facts/Brahmagupta_formula/qweL7FlI">Brahmagupta formula</a></li>
<li><a href="/facts/Brahmagupta_theorem/tJ58g0kr">Brahmagupta theorem</a></li></ul></li>
<li><a href="/facts/Combinatorics/k14xUoKT">Combinatorics</a> – the <a href="/facts/Vy%25C4%2581khy%25C4%2581praj%25C3%25B1apti/rEueEfgL">Bhagavati Sutra</a> had the first mention of a combinatorics problem; the problem asked how many possible combinations of tastes were possible from selecting tastes in ones, twos, threes, etc. from a selection of six different tastes (sweet, pungent, astringent, sour, salt, and bitter). The Bhagavati is also the first text to mention the <a href="/facts/Binomial_coefficient/Tsx7eY5h">choose function</a>.<a class="footnote-ref" id="fnref:279" href="#fn:279">279</a> In the second century BC, <a href="/facts/Pingala/Fb0rL6Ap">Pingala</a> included an enumeration problem in the <a href="/facts/Sanskrit_prosody/6Wjo0MEA">Chanda Sutra</a> (also Chandahsutra) which asked how many ways a six-syllable metre could be made from short and long notes.<a class="footnote-ref" id="fnref:280" href="#fn:280">280</a><a class="footnote-ref" id="fnref:281" href="#fn:281">281</a> Pingala found the number of metres that had 
 
 
 
 n
 
 
 {\displaystyle n}
 
 long notes and 
 
 
 
 k
 
 
 {\displaystyle k}
 
 short notes; this is equivalent to finding the <a href="/facts/Binomial_coefficients/Tsx7eY5h">binomial coefficients</a>.</li>
<li>Jain texts define five different types of <a href="/facts/Infinity/cF506uD7">infinity</a> – the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere, and the infinite perpetually.<a class="footnote-ref" id="fnref:282" href="#fn:282">282</a> and the <a href="/facts/Satkhandagama/PASnFwA7">Satkhandagama</a></li>
<li><a href="/facts/Fibonacci_numbers/mqxpAUQD">Fibonacci numbers</a> – This sequence was first described by <a href="/facts/Virahanka/XWx66hEV">Virahanka</a> (c. 700 CE), Gopāla (c. 1135), and <a href="/facts/Hemachandra/TGl9dvyP">Hemachandra</a> (c. 1150),<a class="footnote-ref" id="fnref:283" href="#fn:283">283</a> as an outgrowth of the earlier writings on Sanskrit prosody by <a href="/facts/Pingala/Fb0rL6Ap">Pingala</a> (c. 200 BCE).</li>
<li><a href="/facts/Madhava%2527s_correction_terms/I9BeAAyp">Madhava's correction terms</a> – Madhava's correction term is a mathematical expression attributed to <a href="/facts/Madhava_of_Sangamagrama/09hFJnVQ">Madhava of Sangamagrama</a> (c. 1340 – c. 1425), the founder of the <a href="/facts/Kerala_school_of_astronomy_and_mathematics/lkJPFMKe">Kerala school of astronomy and mathematics</a>, that can be used to give a better approximation to the value of the mathematical constant π (pi) than the partial sum approximation obtained by truncating the <a href="/facts/Madhava_series/Vng3X9s1">Madhava-Leibniz infinite series</a> for π. The Madhava-Leibniz infinite series for π.</li>
<li><a href="/facts/Pascal%2527s_triangle/tb6BKXbc">Pascal's triangle</a> – Described in the 6th century CE by <a href="/facts/Varahamihira/zgAxCKuR">Varahamihira</a><a class="footnote-ref" id="fnref:284" href="#fn:284">284</a> and in the 10th century by <a href="/facts/Halayudha/Neoa1qEV">Halayudha</a>,<a class="footnote-ref" id="fnref:285" href="#fn:285">285</a> commenting on an obscure reference by <a href="/facts/Pingala/Fb0rL6Ap">Pingala</a> (the author of an earlier work on prosody) to the "Meru-prastaara", or the "Staircase of Mount Meru", in relation to binomial coefficients. (It was also independently discovered in the 10th or 11th century in Persia and China.)</li>
<li>Integral solution to <a href="/facts/Pell%2527s_equation/n0ul61eQ">Pell's equation</a> – About a thousand years before <a href="/facts/John_Pell_(mathematician)/XYuKPrVh">Pell's</a> time, Indian scholar Brahmagupta (598–668 CE) was able to find integral solutions to vargaprakṛiti (Pell's equation):<a class="footnote-ref" id="fnref:286" href="#fn:286">286</a><a class="footnote-ref" id="fnref:287" href="#fn:287">287</a> 
 
 
 
  
 
 x
 
 2
 
 
 −
 N
 
 y
 
 2
 
 
 =
 1
 ,
 
 
 {\displaystyle \ x^{2}-Ny^{2}=1,}
 
 where N is a non-square integer, in his <a href="/facts/Brahmasphutasiddhanta/22p6812L">Brâhma-sphuṭa-siddhânta</a> treatise.<a class="footnote-ref" id="fnref:288" href="#fn:288">288</a></li>
<li>Ardhacheda – Earlier than <a href="/facts/Michael_Stifel/PQMsGL9C">Michael Stifel</a>, the 8th century <a href="/facts/Jain/h0glxhjH">Jain</a> mathematician <a href="/facts/Virasena/2EgyTuau">Virasena</a> is credited with a precursor to the binary logarithm. Virasena's concept of ardhacheda has been defined as the number of times a given number can be divided evenly by two. This definition gives rise to a function that coincides with the binary logarithm on the powers of two,<a class="footnote-ref" id="fnref:289" href="#fn:289">289</a> but it is different for other integers, giving the <a href="/facts/P-adic_order/wktvC3UP">2-adic order</a> rather than the logarithm.<a class="footnote-ref" id="fnref:290" href="#fn:290">290</a></li>
<li><a href="/facts/Ku%25E1%25B9%25AD%25E1%25B9%25ADaka/DyvgKaJR">Kuṭṭaka</a> – The Kuṭṭaka algorithm has much similarity with and can be considered as a precursor of the modern day <a href="/facts/Extended_Euclidean_algorithm/wmomforl">extended Euclidean algorithm</a>. The latter algorithm is a procedure for finding integers x and y satisfying the condition ax + by = <a href="/facts/Greatest_common_divisor/kNFvBuKl">gcd</a>(a, b).<a class="footnote-ref" id="fnref:291" href="#fn:291">291</a></li>
<li><a href="/facts/Differential_calculus/uU1AAc4N">Preliminary differentiation</a> – Preliminary concept of differentiation and the <a href="/facts/Differential_coefficient/kUgJaFLs">differential coefficient</a> were known to <a href="/facts/Bhaskaracharya/BQlUY9gA">bhaskaracharya</a><a class="footnote-ref" id="fnref:292" href="#fn:292">292</a></li></ul>
<h3>Linguistics and Literature</h3>
<ul><li><a href="/facts/Formal_grammar/QLxaQNAz">Formal grammar</a> / <a href="/facts/Formal_systems/KaeDAjK7">Formal systems</a> – In his treatise <a href="/facts/A%25E1%25B9%25A3%25E1%25B9%25AD%25C4%2581dhy%25C4%2581y%25C4%25AB/tFel2l4D">Astadhyayi</a>, <a href="/facts/P%25C4%2581%25E1%25B9%2587ini/C2brRvXB">Panini</a> gives formal production rules and definitions to describe the formal grammar of <a href="/facts/Sanskrit/ychfjhlx">Sanskrit</a>.<a class="footnote-ref" id="fnref:293" href="#fn:293">293</a> In <a href="/facts/Formal_language/crDTyP8q">formal language theory</a>, a grammar (when the context is not given, often called a formal grammar for clarity) is a set of <a href="/facts/Production_(computer_science)/J7E2FXKs">production rules</a> for <a href="/facts/String_(computer_science)/4ChJu5WS">strings</a> in a <a href="/facts/Formal_language/crDTyP8q">formal language</a>. The rules describe how to form strings from the language's <a href="/facts/Alphabet_(computer_science)/6KW9qYRW">alphabet</a> that are valid according to the language's <a href="/facts/Syntax_(programming_languages)/zM5oInza">syntax</a>. A grammar does not describe the <a href="/facts/Semantics/1L4WwLAP">meaning of the strings</a> or what can be done with them in whatever context—only their form. The <a href="/facts/Backus-Naur_form/xbMXDntc">Backus-Naur form</a>, used to describe the <a href="/facts/Syntax_(programming_languages)/zM5oInza">syntax</a> of programming languages, applies similar concepts.<a class="footnote-ref" id="fnref:294" href="#fn:294">294</a></li>
<li>Sarvatobhadra Palindrome: The most complex palindrome, an example of which is in the <a href="/facts/Shishupala_Vadha/P3VAgYJq">Shishupala Vadha</a> of <a href="/facts/Magha_(poet)/CeGo2dfB">Magha</a>.</li></ul>
<blockquote>

<table><tbody><tr><td>सकारनानारकास-कायसाददसायका ।रसाहवा वाहसार-नादवाददवादना ॥sakāranānārakāsa-kāyasādadasāyakārasāhavā vāhasāra-nādavādadavādanā.</td><td><table><tbody><tr><td>sa</td><td>kā</td><td>ra</td><td>nā</td><td>nā</td><td>ra</td><td>kā</td><td>sa</td></tr><tr><td>kā</td><td>ya</td><td>sā</td><td>da</td><td>da</td><td>sā</td><td>ya</td><td>kā</td></tr><tr><td>ra</td><td>sā</td><td>ha</td><td>vā</td><td>vā</td><td>ha</td><td>sā</td><td>ra</td></tr><tr><td>nā</td><td>da</td><td>vā</td><td>da</td><td>da</td><td>vā</td><td>da</td><td>nā</td></tr><tr><td colspan="8">(and the lines reversed)</td></tr><tr><td>nā</td><td>da</td><td>vā</td><td>da</td><td>da</td><td>vā</td><td>da</td><td>nā</td></tr><tr><td>ra</td><td>sā</td><td>ha</td><td>vā</td><td>vā</td><td>ha</td><td>sā</td><td>ra</td></tr><tr><td>kā</td><td>ya</td><td>sā</td><td>da</td><td>da</td><td>sā</td><td>ya</td><td>kā</td></tr><tr><td>sa</td><td>kā</td><td>ra</td><td>nā</td><td>nā</td><td>ra</td><td>kā</td><td>sa</td></tr></tbody></table></td></tr></tbody></table>
<blockquote>"[That army], which relished battle (rasāhavā) contained allies who brought low the bodes and gaits of their various striving enemies (sakāranānārakāsakāyasādadasāyakā), and in it the cries of the best of mounts contended with musical instruments (vāhasāranādavādadavādanā)."</blockquote>
</blockquote>
Palindromic Novel: The Ramakrishna Vilomakavyam by Dyvagnya Surya Pandita is an example of a narrative that, when read forward, relate the story of the Ramayana and, when read backward, relate the story of the Mahabharata.

<h3>Mining</h3>
<ul><li><a href="/facts/Diamond_(gemstone)/tQxRRr2w">Diamond mining</a> and diamond tools: Diamonds were first recognised and mined in central India,<a class="footnote-ref" id="fnref:295" href="#fn:295">295</a><a class="footnote-ref" id="fnref:296" href="#fn:296">296</a><a class="footnote-ref" id="fnref:297" href="#fn:297">297</a> where significant alluvial deposits of the stone could then be found along the rivers <a href="/facts/Penner_River/wmEH0cJm">Penner</a>, <a href="/facts/Krishna_River/fEmCfqlX">Krishna</a> and <a href="/facts/Godavari_River/rLLkY6kJ">Godavari</a>. It is unclear when diamonds were first mined in India, although estimated to be at least 5,000 years ago.<a class="footnote-ref" id="fnref:298" href="#fn:298">298</a> India remained the world's only source of diamonds until the discovery of diamonds in Brazil in the 18th century.<a class="footnote-ref" id="fnref:299" href="#fn:299">299</a><a class="footnote-ref" id="fnref:300" href="#fn:300">300</a><a class="footnote-ref" id="fnref:301" href="#fn:301">301</a> <a href="/facts/Golconda/VRPGw7fG">Golconda</a> served as an important centre for diamonds in <a href="/facts/Central_India/LqI923yw">central India</a>.<a class="footnote-ref" id="fnref:302" href="#fn:302">302</a> Diamonds then were exported to other parts of the world, including Europe.<a class="footnote-ref" id="fnref:303" href="#fn:303">303</a> Early references to diamonds in India come from <a href="/facts/Sanskrit/ychfjhlx">Sanskrit</a> texts.<a class="footnote-ref" id="fnref:304" href="#fn:304">304</a> The <a href="/facts/Arthashastra/Sm0NRGrW">Arthashastra</a> of <a href="/facts/Kautilya/GPXUmsHn">Kautilya</a> mentions diamond trade in India.<a class="footnote-ref" id="fnref:305" href="#fn:305">305</a> <a href="/facts/Buddhism/G0wsjrSl">Buddhist</a> works dating from the 4th century BCE mention it as a well-known and precious stone but don't mention the details of diamond cutting.<a class="footnote-ref" id="fnref:306" href="#fn:306">306</a> Another Indian description written at the beginning of the 3rd century describes strength, regularity, brilliance, ability to scratch metals, and good refractive properties as the desirable qualities of a diamond.<a class="footnote-ref" id="fnref:307" href="#fn:307">307</a> A Chinese work from the 3rd century BCE mentions: "Foreigners wear it [diamond] in the belief that it can ward off evil influences".<a class="footnote-ref" id="fnref:308" href="#fn:308">308</a> The Chinese, who did not find diamonds in their country, initially used diamonds as a "jade cutting knife" instead of as a jewel.<a class="footnote-ref" id="fnref:309" href="#fn:309">309</a></li>
<li><a href="/facts/Zinc_mining/JbJ7mxjp">Zinc mining</a> and <a href="/facts/Zinc/80b1qgk3">medicinal zinc</a> – Zinc was first smelted from zinc ore in India.<a class="footnote-ref" id="fnref:310" href="#fn:310">310</a> Zinc mines of Zawar, near <a href="/facts/Udaipur/vjJE7MtQ">Udaipur</a>, <a href="/facts/Rajasthan/rC0MvrRD">Rajasthan</a>, were active during early Christian era.<a class="footnote-ref" id="fnref:311" href="#fn:311">311</a><a class="footnote-ref" id="fnref:312" href="#fn:312">312</a> There are references of medicinal uses of zinc in the <a href="/facts/Charaka_Samhita/S8oVMUxQ">Charaka Samhita</a> (300 BCE).<a class="footnote-ref" id="fnref:313" href="#fn:313">313</a> The <a href="/facts/Rasaratna_Samuccaya/Mwgnmydb">Rasaratna Samuccaya</a> which dates back to the Tantric period (c. 5th – 13th century CE) explains the existence of two types of ores for zinc metal, one of which is ideal for metal extraction while the other is used for medicinal purpose.<a class="footnote-ref" id="fnref:314" href="#fn:314">314</a><a class="footnote-ref" id="fnref:315" href="#fn:315">315</a> India was to melt the first derived from a long experience of the old alchemy zinc by the distillation process, an advanced technique. The ancient Persians had also tried to reduce zinc oxide in an open stove, but had failed. Zawar in Tiri valley of Rajasthan is the first known old zinc smelting site in the world. The distillation technique of zinc production dates back to the 12th century CE and is an important contribution of India in the world of science.</li></ul>
<h3>Space</h3>
<ul><li><a href="/facts/Earth%2527s_orbit/BGGCdFag">Earth's orbit</a> (<a href="/facts/Sidereal_year/BoaRsTrp">Sidereal year</a>): The <a href="/facts/Hindu/D7TFhcg1">Hindu</a> cosmological time cycles explained in the <a href="/facts/Surya_Siddhanta/QVys8ARk">Surya Siddhanta</a> (c.600 CE), give the average length of the sidereal year (the length of the Earth's revolution around the Sun) as 365.2563627 days, which is only a negligible 1.4 seconds longer than the modern value of 365.256363004 days.<a class="footnote-ref" id="fnref:316" href="#fn:316">316</a><a class="footnote-ref" id="fnref:317" href="#fn:317">317</a></li>
<li><a href="/facts/Gravity/bqAN7DdQ">Preliminary concept of gravity</a> – The concept of gravity as attracting objects towards Earth was already known to Greek scholars, <a href="/facts/Brahmagupta/f7uxKXo4">Brahmagupta</a> in sixth century CE also described gravity as an attractive force, using the term gurutvākarṣaṇa in which heavier objects attract towards the earth.<a class="footnote-ref" id="fnref:318" href="#fn:318">318</a><a class="footnote-ref" id="fnref:319" href="#fn:319">319</a><a class="footnote-ref" id="fnref:320" href="#fn:320">320</a></li>
<li><a href="/facts/Periodic_comet/35UuHPYc">Periodicity of comets</a> – Indian astronomers by the 6th century CE believed that comets were apparitions that re-appeared periodically. This was the view expressed in the 6th century by the astronomers <a href="/facts/Varahamihira/zgAxCKuR">Varahamihira</a> and Bhadrabahu, and the 10th-century astronomer <a href="/facts/Bhattotpala/WEsv2egX">Bhattotpala</a> listed the names and estimated periods of certain comets, but it is unfortunately not known how these figures were calculated or how accurate they were.<a class="footnote-ref" id="fnref:321" href="#fn:321">321</a></li>
<li><a href="/facts/Tychonic_system/nRqoQu2K">Tychonic system</a> – A similar model was implicitly mentioned in the Hindu astronomical treatise <a href="/facts/Tantrasamgraha/kkv6oHQC">Tantrasamgraha</a> (c. 1500 CE) by <a href="/facts/Nilakantha_Somayaji/myYT4wWb">Nilakantha Somayaji</a> of the <a href="/facts/Kerala_school_of_astronomy_and_mathematics/lkJPFMKe">Kerala school of astronomy and mathematics</a>.<a class="footnote-ref" id="fnref:322" href="#fn:322">322</a><a class="footnote-ref" id="fnref:323" href="#fn:323">323</a></li>
<li>Reduction of the <a href="/facts/Ecliptic/cJxXDDDW">ecliptic</a>: <a href="/facts/Achyutha_Pisharadi/x7SJ5YvR">Achyutha Pisharadi</a> discovered the techniques.<a class="footnote-ref" id="fnref:324" href="#fn:324">324</a></li></ul>
<h3>Miscellaneous</h3>
<ul><li><a href="/facts/Punch_(drink)/QJfwmh2M">Punch (drink)</a> a <a href="/facts/Mixed_drink/kLQmukCl">mixed drink</a> containing fruits or fruit juice that can be both alcoholic and non-alcoholic originated in the Indian subcontinent before making its way into England by passage through the <a href="/facts/East_India_Company/jpfw533d">East India Company</a>.<a class="footnote-ref" id="fnref:325" href="#fn:325">325</a> This beverage is very popular among the world with many varietal flavors and brands throughout the <a href="/facts/Beverage_industry/QCS1QMdJ">beverage industry</a>.</li>
<li><a href="/facts/Hookah/z2bLAjd5">Hookah</a> or water pipe: according to Cyril Elgood (PP.41, 110), the physician Irfan Shaikh, at the court of the Mughal emperor <a href="/facts/Akbar/e92T534P">Akbar</a> I (1542–1605) invented the Hookah or water pipe used most commonly for smoking <a href="/facts/Tobacco/bTD4RUPQ">tobacco</a>.<a class="footnote-ref" id="fnref:326" href="#fn:326">326</a><a class="footnote-ref" id="fnref:327" href="#fn:327">327</a><a class="footnote-ref" id="fnref:328" href="#fn:328">328</a><a class="footnote-ref" id="fnref:329" href="#fn:329">329</a></li></ul>
<h2 id="modern-india">Modern India</h2>
<h3>Medicine</h3>
<ul><li>NexCAR19, is designed to target cancer cells carrying the CD19 protein, a marker on cancer cells, enhancing precision in treatment.<a class="footnote-ref" id="fnref:330" href="#fn:330">330</a></li>
<li><a href="/facts/Urea/6j84AoCG">Urea</a> stibamine – Sir <a href="/facts/Upendranath_Brahmachari/EWVnzAHI">Upendranath Brahmachari</a> synthesised <a href="/facts/Urea/6j84AoCG">urea</a>-stibamine (carbostibamide) in 1922 and determined that it was an effective treatment for <a href="/facts/Kala-azar/bu6ne799">kala-azar</a> (visceral leishmaniasis).</li>
<li><a href="/facts/Post-kala-azar_dermal_leishmaniasis/emUJkK5S">post-kala-azar dermal leishmaniasis</a> – n 1922, Brahmachari also discovered a new, deadly form of <a href="/facts/Leishmaniasis/L5v8Thy1">leishmaniasis</a>. He called it dermal leishmanoid, marked by the appearance of sudden eruptions on the face of the patients without fever or other complaints. He observed it as a disease in partially cured cases of kala-azar, along with those who had no history of the disease at all.<a class="footnote-ref" id="fnref:331" href="#fn:331">331</a> It has since been termed as <a href="/facts/Post-kala-azar_dermal_leishmaniasis/emUJkK5S">post-kala-azar dermal leishmaniasis</a>.</li>
<li><a href="/facts/Oral_rehydration_therapy/MP7ecgrJ">Oral Rehydrated Solution (ORS)</a>, In 1952 <a href="/facts/Hemendra_Nath_Chatterjee/qVD2vTs3">Hemendra Nath Chatterjee</a><a class="footnote-ref" id="fnref:332" href="#fn:332">332</a> was an Indian scientist from West Bengal known for the earliest publication of a formula for Orally Rehydrated Saline (ORS) for diarrhea.<a class="footnote-ref" id="fnref:333" href="#fn:333">333</a> According to his paper,<a class="footnote-ref" id="fnref:334" href="#fn:334">334</a> he treated 186 patients with his oral glucose with an oral glucose-sodium electrolyte solution and was able to rehydrate his patients with mild to moderately severe cholera.</li>
<li><a href="/facts/Cholera_toxin/9VpdR8Rt">Cholera toxin</a> – Cholera toxin was discovered in 1959 by Indian microbiologist <a href="/facts/Sambhu_Nath_De/cQXR45Hw">Sambhu Nath De</a>.<a class="footnote-ref" id="fnref:335" href="#fn:335">335</a></li>
<li><a href="/facts/In_vitro_fertilisation/kQNMtaBu">In vitro fertilisation</a> – the second successful birth of a 'test tube baby' occurred in India just 67 days after Louise Brown was born. The girl, named Durga, was conceived in vitro using a method developed independently by <a href="/facts/Subhash_Mukhopadhyay_(physician)/NahfLBcf">Subhash Mukhopadhyay</a>, a physician and researcher from <a href="/facts/Kolkata/k0HVgEYm">Kolkata</a>. Mukhopadhyay had been performing experiments on his own with primitive instruments and a household refrigerator.<a class="footnote-ref" id="fnref:336" href="#fn:336">336</a> However, state authorities prevented him from presenting his work at scientific conferences,<a class="footnote-ref" id="fnref:337" href="#fn:337">337</a> and it was many years before Mukhopadhyay's contribution was acknowledged in works dealing with the subject.<a class="footnote-ref" id="fnref:338" href="#fn:338">338</a>[better source needed]</li>
<li><a href="/facts/Cervical_cerclage/xtV6eSoC">Cervical cerclage</a> – was first described by <a href="/facts/V._N._Shirodkar/kVCwjymb">V. N. Shirodkar</a> in <a href="/facts/Bombay/BdoEc10R">Bombay</a> in 1955.<a class="footnote-ref" id="fnref:339" href="#fn:339">339</a></li></ul>
<h3>Electronics and communications</h3>
<ul><li><a href="/facts/Ashwin_Gumaste/aDUWWE3v">Carrier Ethernet Switch Router (CESR)</a> are high capacity routers which provides carrier class ethernet service, developed by IIT Bombay in 2011 and technology was transferred to <a href="/facts/Electronics_Corporation_of_India/mvJEmTCY">ECIL</a>.<a class="footnote-ref" id="fnref:340" href="#fn:340">340</a><a class="footnote-ref" id="fnref:341" href="#fn:341">341</a><a class="footnote-ref" id="fnref:342" href="#fn:342">342</a></li>
<li>Direct-to-Mobile (D2M) technology, developed by Saankya Labs and IIT Kanpur, This tech will enable mobile users to stream videos on their smartphones without an active internet connection.<a class="footnote-ref" id="fnref:343" href="#fn:343">343</a></li>
<li><a href="/facts/Horn_antenna/kVroJAmN">Horn antenna</a> or microwave horn, One of the first horn antennas was constructed by <a href="/facts/Jagadish_Chandra_Bose/r2W5xbXS">Jagadish Chandra Bose</a> in 1897.<a class="footnote-ref" id="fnref:344" href="#fn:344">344</a><a class="footnote-ref" id="fnref:345" href="#fn:345">345</a></li>
<li><a href="/facts/Microwave/HmVSN31Y">Microwave</a>-Indian physicist Jagadish Chandra Bose performed the first experiments with microwaves.<a class="footnote-ref" id="fnref:346" href="#fn:346">346</a></li>
<li><a href="/facts/Radio/XFr909M2">Radiowave communication</a> – In November 1894, the Indian physicist, <a href="/facts/Jagadish_Chandra_Bose/r2W5xbXS">Jagadish Chandra Bose</a>, demonstrated publicly the use of radio waves in <a href="/facts/Kolkata/k0HVgEYm">Calcutta</a>.<a class="footnote-ref" id="fnref:347" href="#fn:347">347</a><a class="footnote-ref" id="fnref:348" href="#fn:348">348</a></li>
<li>Low Mobility Large cell (LMLC), is a feature of 5G and is designed to enhance the signal transmission range of a basestation several times, helping service providers cost-effectively expand coverage in rural areas.<a class="footnote-ref" id="fnref:349" href="#fn:349">349</a></li>
<li><a href="/facts/Waveguide/tJS9Y0GH">Waveguide</a> – <a href="/facts/Jagadish_Chandra_Bose/r2W5xbXS">Jagadish Chandra Bose</a> researched <a href="/facts/Millimetre_wave/l28Grdmp">millimetre wavelengths</a> using waveguides, and in 1897 described to the Royal Institution in London his research carried out in Kolkata.<a class="footnote-ref" id="fnref:350" href="#fn:350">350</a></li>
<li>Phantom connectivity, a system for providing a higher level security to data communication in computer networks developed by <a href="/facts/ISRO/CdAoFQTL">ISRO</a>. Phantom connectivity model enables organization to copy users download data from Internet to Intranet without connecting both the networks.<a class="footnote-ref" id="fnref:351" href="#fn:351">351</a></li></ul>
<h3>Computers and programming languages</h3>
<ul><li>Autolay, is an interactive GUI CAD software for the design of aircraft composite components developed by <a href="/facts/Aeronautical_Development_Agency/7ekSt9Ql">Aeronautical Development Agency</a>, this tool was developed in late 1980's and used by all big aerospace companies such as <a href="/facts/Boeing/tF5sMe9F">Boeing</a>, <a href="/facts/Airbus/PSLf3cM8">Airbus</a> and <a href="/facts/Dassault_Syst%25C3%25A8mes/VXPYV4nM">Dassault Systèmes</a><a class="footnote-ref" id="fnref:352" href="#fn:352">352</a><a class="footnote-ref" id="fnref:353" href="#fn:353">353</a></li>
<li>Fragalyst, is a software for analysis of fragments from an explosion or blast developed by <a href="/facts/Central_Institute_of_Mining_and_Fuel_Research/K39QatDh">CSIR-CIMFR</a>, the technology allows us to visualize the blast & fragments in a computer GUI.<a class="footnote-ref" id="fnref:354" href="#fn:354">354</a><a class="footnote-ref" id="fnref:355" href="#fn:355">355</a></li>
<li><a href="/facts/Haptik/8SAIkweK">chatbot-based conversational AI</a>, one of early modern AI/ML based chatbot was released by <a href="/facts/Haptik/8SAIkweK">Haptik.ai</a> in 2013, when chatbots were not common.<a class="footnote-ref" id="fnref:356" href="#fn:356">356</a><a class="footnote-ref" id="fnref:357" href="#fn:357">357</a><a class="footnote-ref" id="fnref:358" href="#fn:358">358</a></li>
<li><a href="/facts/Visual_J_Sharp/J8s8qupu">Visual J#</a> – A transitional <a href="/facts/Programming_language/cWTYbgWa">programming language</a> for programmers of <a href="/facts/Java_(programming_language)/9ScgFyAL">Java</a> and <a href="/facts/Visual_J%252B%252B/7zblb4Pm">Visual J++</a> languages, so they could use their existing knowledge and applications on <a href="/facts/.NET_Framework/J6QDAUhP">.NET Framework</a>. It was developed by the <a href="/facts/Hyderabad%2c_Telangana/APPUtNqU">Hyderabad</a>-based <a href="/facts/HITEC_City/J2oxY2br">Microsoft India Development Center at HITEC City</a> in India.<a class="footnote-ref" id="fnref:359" href="#fn:359">359</a><a class="footnote-ref" id="fnref:360" href="#fn:360">360</a></li>
<li><a href="/facts/Julia_(programming_language)/AoB0PJ9C">Julia</a> is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. <a href="/facts/Viral_B._Shah/NGsaycjv">Viral B. Shah</a> an Indian computer scientist contributed to the development of the language in Bangalore while also actively involved in the initial design of the Aadhaar project in India using <a href="/facts/India_Stack/YqFTKY4K">India Stack</a>.<a class="footnote-ref" id="fnref:361" href="#fn:361">361</a></li>
<li><a href="/facts/Kojo_(programming_language)/o8VT7Ivm">Kojo</a> – A <a href="/facts/Programming_language/cWTYbgWa">programming language</a> and <a href="/facts/Integrated_development_environment/jbEINSQf">integrated development environment</a> (IDE) for computer programming and learning. Kojo is an <a href="/facts/Open-source_software/HzTaB8E9">open-source software</a>. It was created, and is actively developed, by Lalit Pant, a computer programmer and teacher living in <a href="/facts/Dehradun/zRaoaVtl">Dehradun</a>, India.<a class="footnote-ref" id="fnref:362" href="#fn:362">362</a><a class="footnote-ref" id="fnref:363" href="#fn:363">363</a></li>
<li><a href="/facts/RISC-V/pUSKDat1">RISC-V</a> ISA (microprocessor) implementations (a US standard, not from India, but some implementations are such as those below):
<ul><li><a href="/facts/SHAKTI_(microprocessor)/DsRvEeXh">SHAKTI</a> – Open Source, Bluespec System <a href="/facts/Verilog/efVqbKXg">Verilog</a> definitions, for FinFET implementations of the ISA, have been created at <a href="/facts/IIT_Madras/LC6q9DdR">IIT Madras</a>, and are hosted on <a href="/facts/GitLab/3CCW9luS">GitLab</a>.<a class="footnote-ref" id="fnref:364" href="#fn:364">364</a></li>
<li><a href="/facts/VEGA_Microprocessors/ddvpSpqI">VEGA Microprocessors</a> – India's first indigenous 64-bit, superscalar, out-of-order, multi-core RISC-V Processor design, developed by <a href="/facts/C-DAC/nnJTNzpl">C-DAC</a>.<a class="footnote-ref" id="fnref:365" href="#fn:365">365</a></li></ul></li>
<li><a href="/facts/File_Transfer_Protocol/THuWgzfw">File Transfer Protocol</a> (FTP) – A standard communication protocol used for the transfer of computer files from a server to a client on a computer network. FTP is built on a client–server model architecture using separate control and data connections between the client and the server. <a href="/facts/Abhay_Bhushan/401SJ4dG">Abhay Bhushan</a> is the author of the File Transfer Protocol (which he started working on while he was a student at IIT-Kanpur) and the early versions of email protocols<a class="footnote-ref" id="fnref:366" href="#fn:366">366</a></li>
<li><a href="/facts/TCS_BaNCS/HsRCdDSu">TCS BaNCS</a>, was one of the first core banking software started implemented in late 1970s and released in early 80s.</li></ul>
<h3>Construction, civil engineering and architecture</h3>
<ul><li>Coal Mine to PSP, <a href="/facts/Coal_India/GYpK4p5P">Coal India</a> will turn abandoned mines or de-coaled mine to <a href="/facts/Pumped-storage_hydroelectricity/j15NI2UV">Pumped Storage Projects(PSP)</a> with help of <a href="/facts/NHPC/qUu4WUhS">NHPC</a> hence saving huge amount of capital for development of reservoir or dams.<a class="footnote-ref" id="fnref:367" href="#fn:367">367</a></li>
<li>CO2-treated-C&D, researchers at the Centre for Sustainable Technologies (CST), IISc, are exploring ways to store carbon dioxide from industrial flue gas in excavated soil in Construction and Demolition (C&D) waste. the effect of injecting carbon dioxide gas into clayey soil—typically excavated from construction sites. This resulted in better stabilization of clay by cement and lime, and reduced the surface area, pore volume and lime reactivity of clay in soil, thereby improving the bulk engineering performance of the material.<a class="footnote-ref" id="fnref:368" href="#fn:368">368</a><a class="footnote-ref" id="fnref:369" href="#fn:369">369</a></li>
<li>Rib & spine/Spine & Wing technique, <a href="/facts/National_Highways_Authority_of_India/mpoveXNJ">NHAI</a> has developed a flyover design which allows to save cost, time, minimum material usage and allows light under the flyover using the same technique.</li>
<li>(I)-TM Tunneling technique:(I)-TM as Himalayan tunnelling method for tunnelling through the Himalayan geology to build tunnels in Jammu and Kashmir. Engineers decided to provide rigid supports using 'ISHB' as against the lattice girder method used in the New Austrian Tunnelling Method.ISHB uses nine-metre pipes in the mountains. It is called pipe roofing. Engineers made an umbrella using these perforated poles and filled them with PU grout.<a class="footnote-ref" id="fnref:370" href="#fn:370">370</a><a class="footnote-ref" id="fnref:371" href="#fn:371">371</a><a class="footnote-ref" id="fnref:372" href="#fn:372">372</a></li>
<li>waterproof roads, zydex industries has developed waterproof road by forming a skin like layer that is water resistant using inhouse silane nanotechnology.<a class="footnote-ref" id="fnref:373" href="#fn:373">373</a><a class="footnote-ref" id="fnref:374" href="#fn:374">374</a></li>
<li><a href="/facts/Plastic_road/WQf0WAht">Plastic road</a> are made entirely of plastic or of composites of plastic with other materials. Plastic roads are different from standard roads in the respect that standard roads are made from asphalt concrete, which consists of mineral aggregates and asphalt. Most plastic roads sequester <a href="/facts/Plastic_waste/oLNNHQrG">plastic waste</a> within the asphalt as an aggregate. Plastic roads first developed by <a href="/facts/Rajagopalan_Vasudevan/NsncxUyP">Rajagopalan Vasudevan</a> in 2001<a class="footnote-ref" id="fnref:375" href="#fn:375">375</a><a class="footnote-ref" id="fnref:376" href="#fn:376">376</a><a class="footnote-ref" id="fnref:377" href="#fn:377">377</a></li>
<li><a href="/facts/Steel/aN6qWo4H">Steel</a> <a href="/facts/Slag/LD3qEAlV">slag</a> <a href="/facts/Road/3aadH4s3">road</a>, world's first steel slag road NH-66 was constructed by <a href="/facts/Central_Road_Research_Institute/saS5fzJb">Central Road Research Institute</a> under CSIR.<a class="footnote-ref" id="fnref:378" href="#fn:378">378</a><a class="footnote-ref" id="fnref:379" href="#fn:379">379</a><a class="footnote-ref" id="fnref:380" href="#fn:380">380</a><a class="footnote-ref" id="fnref:381" href="#fn:381">381</a></li></ul>
<h3>Food</h3>
<ul><li><a href="/facts/Butter_chicken/pgBV0oNG">Butter chicken</a>, was invented in <a href="/facts/Moti_Mahal_(restaurant)/zRjVLwaI">Moti Mahal</a> restaurant in Daryaganj of <a href="/facts/New_Delhi/9UMpnDN8">Delhi</a> in 1950's.</li>
<li><a href="/facts/List_of_instant_foods/n7jtdttI">Instant</a> <a href="/facts/Momo_(food)/2AsJVMtR">momos</a> popularly known as Frozen Momos, Prasuma introduced the worlds's first instant momos that can be prepared using oil and hot water similar to Noodles.<a class="footnote-ref" id="fnref:382" href="#fn:382">382</a><a class="footnote-ref" id="fnref:383" href="#fn:383">383</a><a class="footnote-ref" id="fnref:384" href="#fn:384">384</a></li></ul>
<h3>Finance and banking</h3>
<ul><li><a href="/facts/Payments_bank/5nXNYRae">Payments bank</a> is an Indian new model of banks conceptualised by the Reserve Bank of India (RBI) without issuing credit.</li></ul>
<h3>Paleontology</h3>
<ul><li>In 2024, one of the longest snakes to ever exist, <a href="/facts/Vasuki_indicus/sw7gdwnD">Vasuki indicus</a>, was discovered by scientists from the <a href="/facts/Indian_Institutes_of_Technology/ytm1MuBU">Indian Institute of Technology</a>. The snake was estimated to be between 10.9 and 15.2 metres in length and lived 47 million years ago. The fossilised vertebrae of Vasuki indicus were discovered in a lignite mine in <a href="/facts/Gujarat/HwmVfMwr">Gujarat</a>. It was likely a slow moving predator who killed its prey through constriction.<a class="footnote-ref" id="fnref:385" href="#fn:385">385</a></li>
<li>In 2018, scientists from the <a href="/facts/Geological_Survey_of_India/zYrqWwP9">Geological Survey of India</a> and the Indian Institute of Technology discovered the fossil remains of a previously unknown dinosaur species in the <a href="/facts/Thar_Desert/uREh2fC8">Thar Desert</a> region of Jaisalmer, Rajasthan. The dinosaur is named <a href="/facts/Tharosaurus_indicus/DgwzbXMf">Tharosaurus indicus</a>, after the Thar Desert and India.<a class="footnote-ref" id="fnref:386" href="#fn:386">386</a></li></ul>
<h3>Zoology</h3>
<ul><li>The world's first white tiger was Mohan, a mutant Bengal tiger captured in 1951 by Maharaja Martand Singh of Rewa. These type of tiger are found in <a href="/facts/White_Tiger_Safari_%2526_Zoo_Mukundpur/jFgEo5Ij">White Tiger Safari & Zoo Mukundpur</a></li></ul>
<h3>Genetics</h3>
<ul><li><a href="/facts/Amrapali_(mango)/ctvWDsYu">Amrapali</a> mango – A named mango cultivar introduced in 1971 by Dr. Pijush Kanti Majumdar at the Indian Agriculture Research Institute in Delhi.</li>
<li>Asmon, is a plant based drug that is used to treat bronchial asthma developed by <a href="/facts/Council_of_Scientific_and_Industrial_Research/2tDChQJu">CSIR</a>.<a class="footnote-ref" id="fnref:387" href="#fn:387">387</a></li>
<li>Mynvax – The world's first "warm" COVID-19 vaccine, developed by <a href="/facts/Indian_Institute_of_Science/GNxvFXWn">IISc</a>, capable of withstanding 37 °C (99 °F) for a month and neutralise all coronavirus variants of concern.<a class="footnote-ref" id="fnref:388" href="#fn:388">388</a></li>
<li><a href="/facts/ZyCoV-D/257npdaD">ZyCoV-D</a> vaccine – The world's first DNA-based vaccine for humans.<a class="footnote-ref" id="fnref:389" href="#fn:389">389</a></li></ul>
<h3>Metallurgy, manufacturing, and industry</h3>
<ul><li>Carbon nitride solar reactor – In September 2021, A team from the <a href="/facts/Institute_of_Nano_Science_and_Technology/lUcpGhwY">Institute of Nano Science and Technology (INST), Mohali</a>, has fabricated a prototype reactor which operates under natural sunlight to produce hydrogen at a scale of around 6.1 litres in eight hours. They have used an earth-abundant chemical called carbon nitrides as a catalyst for the purpose.<a class="footnote-ref" id="fnref:390" href="#fn:390">390</a><a class="footnote-ref" id="fnref:391" href="#fn:391">391</a></li>
<li><a href="/facts/National_Metallurgical_Laboratory/fJKds6Bt">NML Magnetherm process</a> is a large scale magnesium producing process, it is a kind of electrothermal process that produces at pilot scale of 300-450 kg raw material producing ~40 kg Magnesium/batch. A pilot plant is being constructed at Jamshedpur for using this process. <a class="footnote-ref" id="fnref:392" href="#fn:392">392</a><a class="footnote-ref" id="fnref:393" href="#fn:393">393</a></li>
<li>Contactless Handwasher, is a device which provides automated touchless handwashing process, major advantage of this type of system is that it uses very less water and hand Washing for 2000 people requires only one soap refill.It was developed by <a href="/facts/Central_Mechanical_Engineering_Research_Institute/jsdWSBBF">CSIR-CMERI</a>.<a class="footnote-ref" id="fnref:394" href="#fn:394">394</a></li>
<li>Hydrogen DRI steel, Jindal Steel is making world's first hydrogen based DRI process in its steel plants in Angul.<a class="footnote-ref" id="fnref:395" href="#fn:395">395</a><a class="footnote-ref" id="fnref:396" href="#fn:396">396</a><a class="footnote-ref" id="fnref:397" href="#fn:397">397</a><a class="footnote-ref" id="fnref:398" href="#fn:398">398</a></li>
<li>High ash coal gasification (coal to methanol) – The central government gave the country world's first 'coal to methanol' (CTM) plant built by the <a href="/facts/Bharat_Heavy_Electricals_Limited/DRWFNbMa">Bharat Heavy Electricals Limited</a> (BHEL). The plant was inaugurated in BHEL's Hyderabad unit, The pilot project is the first that uses the gasification method for converting high-ash coal into methanol. Handling of high ash and heat required to melt this high amount of ash is a challenge in the case of Indian coal, which generally has high ash content. Bharat Heavy Electricals Limited has developed the fluidized bed gasification technology suitable for high ash Indian coals to produce syngas and then convert syngas to methanol with 99% purity.<a class="footnote-ref" id="fnref:399" href="#fn:399">399</a></li>
<li><a href="/facts/Magnetically_controlled_shunt_reactor/11hbsU9L">Controlled shunt reactor</a> – In 2002, <a href="/facts/Bharat_Heavy_Electricals_Limited/DRWFNbMa">Bharat Heavy Electricals Limited</a> has successfully developed a first-of-its-kind in the world device for improving power transfer capability and reducing transmission losses in the country's highest rating (400 kV) transmission lines.The device is called Controlled Shunt Reactor.<a class="footnote-ref" id="fnref:400" href="#fn:400">400</a><a class="footnote-ref" id="fnref:401" href="#fn:401">401</a></li>
<li><a href="/facts/Defence_Metallurgical_Research_Laboratory/t9B9xPb8">DMR 1700</a> steel – For several high-technology applications, such as military hardware and aerospace, need to possess ultrahigh strength (UHS; minimum yield strength of 1380 MPa (200 ksi)) coupled with high fracture toughness in order to meet the requirement of minimum weight while ensuring high reliability.</li>
<li><a href="/facts/Defence_Metallurgical_Research_Laboratory/t9B9xPb8">DMR SN 742</a> is a nickel-based superalloy developed by the Defence Metallurgical Research Laboratory (DMRL) in India. It is specifically designed for aero-engine applications, such as high-pressure compressors (HPC) and turbine rotors (HPT) in gas turbine engines.<a class="footnote-ref" id="fnref:402" href="#fn:402">402</a><a class="footnote-ref" id="fnref:403" href="#fn:403">403</a></li>
<li>GTM-900 is a high-temperature alpha-beta titanium alloy developed by <a href="/facts/National_Aerospace_Laboratories/f9qdpYvP">National Aerospace Laboratories</a> and <a href="/facts/Defence_Metallurgical_Research_Laboratory/t9B9xPb8">DMRL</a> used for components like compressor blades due to its strength and creep resistance at elevated temperatures.<a class="footnote-ref" id="fnref:404" href="#fn:404">404</a><a class="footnote-ref" id="fnref:405" href="#fn:405">405</a></li>
<li>TITAN 26A and TITAN 29A, These are high-performance titanium-based alloys which are known for their high strength, creep resistance, and corrosion resistance, particularly in high-temperature environments.<a class="footnote-ref" id="fnref:406" href="#fn:406">406</a></li>
<li>Magnesium-lithium alloy grade(Mg-9Li-7.5Al-1.2Sn), ISRO has successfully mastered melting and casting of this alloy using inert atmosphere. It is now possible to melt up to 20 kg of this alloy and gave stable properties up to 1000C.<a class="footnote-ref" id="fnref:407" href="#fn:407">407</a><a class="footnote-ref" id="fnref:408" href="#fn:408">408</a></li>
<li><a href="/facts/Jindal_Stainless_Limited/gSUjM2GP">JD-1</a> alloy – A special lightweight alloy developed by <a href="/facts/Jindal_Stainless_Limited/gSUjM2GP">Jindal Defence</a> with a minimum guaranteed hardness of 500 HB. It can be used in aerospace, small arms, and engineering solutions. It is mainly used in armoured jacket.</li>
<li><a href="/facts/Polymetallic_nodules/e9RCgkFo">Polymetallic nodules</a>, India is considered a pioneer in the exploration of polymetallic nodules, In 1981, Indian scientists recovered manganese nodules, marking the beginning of deep sea exploration in the country.In 1987, India became the first country to receive Pioneer Investor status from the International Seabed Authority (ISA).<a class="footnote-ref" id="fnref:409" href="#fn:409">409</a><a class="footnote-ref" id="fnref:410" href="#fn:410">410</a></li>
<li>Sorption-enhanced steam methane reforming (SESMR) – In April 2022, the scientists from CSIR-Indian Institute of Chemical Technology (CSIR-IICT), Hyderabad developed a fluidized bed reactor (FBR) facility in Hyderabad to perform sorption enhanced steam methane reforming (SESMR) to achieve clean hydrogen in its purest form. The team of scientists have designed a hybrid material to simulate capturing carbon dioxide in-situ (onsite) and converting it into clean hydrogen from non-fuel grade bioethanol.<a class="footnote-ref" id="fnref:411" href="#fn:411">411</a></li>
<li><a href="/facts/Harichand_Megha_Dalaya/q8bIeHsm">Spray-drying buffalo milk</a> – The collective consensus of dairy experts worldwide was that buffalo milk could not be spray-dried due to its high fat content. Harichand Megha Dalaya & his invention of the spray dry equipment, led to the world's first buffalo milk spray-dryer, at Amul Dairy in Gujarat.</li>
<li><a href="/facts/Neem-coated_urea/BNxGzaCQ">Neem-coated urea</a> is an agriculture fertilizer in which the urea is neem oil-coated. The coating of neem slows the nitrification of urea thereby helps in increased absorption of nutrients in the soil as well as reduces groundwater pollution.<a class="footnote-ref" id="fnref:412" href="#fn:412">412</a></li>
<li>Jackal steel – An advanced grade high-strength, low-alloy steel. The technology of Jackal steel has been passed on to Steel Authority of India Limited (SAIL) and MIDHANI for its bulk production.</li>
<li>High-Rise Pantograph – The new-design world record pantograph, developed completely in-house for use in DFC & other freight routes with height of 7.5 metres (25 ft).<a class="footnote-ref" id="fnref:413" href="#fn:413">413</a></li>
<li>Commercial <a href="/facts/Carbon_capture_and_utilization/C195chLm">CCU</a> plant: Tuticorin Alkali Chemicals and Fertilizers Limited (TFL) partnered with Carbon Clean to create the world's first fully commercial CCU plant. The 10 MW facility captures coal-fired boiler flue gas and uses it to deliver industrial quality CO2. The 10 MW facility captures coal-fired boiler flue gas and uses it to deliver industrial quality CO2.<a class="footnote-ref" id="fnref:414" href="#fn:414">414</a> The technology has been developed by Carbon Clean Solutions, headquartered in London – a start-up by two Indian engineers focusing on carbon dioxide separation technology.There are many chemicals exported out of India where CO2 is the raw material.<a class="footnote-ref" id="fnref:415" href="#fn:415">415</a></li>
<li>Triple-stack container freight train<a class="footnote-ref" id="fnref:416" href="#fn:416">416</a><a class="footnote-ref" id="fnref:417" href="#fn:417">417</a> – In order to ensure new streams of traffic and commodities and to bring about a modal shift, the DFC is undertaking trials for running smaller than usual containers, known as dwarf containers (where the container height is lower by 660 mm than normal containers), in triple-stack formation to further improve the profitability of train operations. It may be possible to run these as double-stack on conventional routes and triple-stack on routes with high-rise OHE, once the trials are successfully completed.<a class="footnote-ref" id="fnref:418" href="#fn:418">418</a></li></ul>
<h3>Metrology</h3>

<ul><li><a href="/facts/Crescograph/ahFKEwdy">Crescograph</a> – The crescograph, a device for measuring growth in plants, was invented in the early 20th century by the Bengali scientist Sir <a href="/facts/Jagadish_Chandra_Bose/r2W5xbXS">Jagadish Chandra Bose</a>.<a class="footnote-ref" id="fnref:419" href="#fn:419">419</a><a class="footnote-ref" id="fnref:420" href="#fn:420">420</a></li>
<li><a href="/facts/Shearing_interferometer/5j7FfMfv">Shearing interferometer</a> – Invented by M.V.R.K. Murty, a type of Lateral <a href="/facts/Shearing_Interferometer/5j7FfMfv">Shearing Interferometer</a> utilises a laser source for measuring refractive index.<a class="footnote-ref" id="fnref:421" href="#fn:421">421</a><a class="footnote-ref" id="fnref:422" href="#fn:422">422</a></li></ul>
<h3>Rocket science and jet propulsion</h3>
<ul><li><a href="/facts/Rohini_(rocket_family)/NAMvnaEE">Air-breathing rocket</a>, On 23 July 2024 ISRO successfully fired world's first air-breathing rocket, using a modified Rohini 560 rocket.<a class="footnote-ref" id="fnref:423" href="#fn:423">423</a><a class="footnote-ref" id="fnref:424" href="#fn:424">424</a><a class="footnote-ref" id="fnref:425" href="#fn:425">425</a></li>
<li><a href="/facts/Solid_Fuel_Ducted_Ramjet/QplFsufw">Solid Fuel Ducted Ramjet</a>, is a jet propulsion technology which uses solid propellant, developed by <a href="/facts/Defence_Research_and_Development_Organisation/HYTLS49D">Defence Research and Development Organisation</a>.</li>
<li><a href="/facts/Small_Satellite_Launch_Vehicle/Wxsr06H0">Small Satellite Launch Vehicle</a>, is a multi-stage solid propellent rocket that is cost-effective and very less complex used to deliver micro-satellites less than 500 kg weight. it is innovative as its three stages are solid propellent making it very efficient.<a class="footnote-ref" id="fnref:426" href="#fn:426">426</a></li></ul>
<h3>Science and technology</h3>
<ul><li>Bipyrazole Organic Crystals, the piezoelectric molecules developed by <a href="/facts/Indian_Institutes_of_Science_Education_and_Research/EjxtnR3X">IISER</a> scientists recombine following mechanical fracture without any external intervention, autonomously self-healing in milliseconds with crystallographic precision.<a class="footnote-ref" id="fnref:427" href="#fn:427">427</a></li>
<li>SEBEX 2, is a high performance explosive, it is said to be 2.01 times more lethal than TNT and most powerful non-nuclear explosives in the world. The Indian Navy has certified the explosive.<a class="footnote-ref" id="fnref:428" href="#fn:428">428</a></li>
<li><a href="/facts/Magnetic/eo75vApl">magnetic</a> <a href="/facts/Superatoms/xLQfACI0">superatoms</a>, In 2009 a team of Harish Chandra Research Institute, Allahabad discovered magnetic superatoms.<a class="footnote-ref" id="fnref:429" href="#fn:429">429</a><a class="footnote-ref" id="fnref:430" href="#fn:430">430</a><a class="footnote-ref" id="fnref:431" href="#fn:431">431</a></li>
<li><a href="/facts/Silica_fiber/h8wjmF4o">Silica fiber based composite</a> or Silica-Silica composite, In 2012 <a href="/facts/ISRO/CdAoFQTL">ISRO</a> developed world's first pure silica fiber composite without carbon element known as silica fiber-silica matrix composite and also a new technology for developing silica fibres by sol-gel process. These fibres can be used for high temperature insulation up to 1500C and cheaper than Carbon fiber composite. Silica-silica composite are prepared by leaching glass cloth with hydrochloric acid, rinsing to remove acid therefrom, vacuum drying, moulding and treating with ethyl silicate and cationic starch binder further drying and sintering.<a class="footnote-ref" id="fnref:432" href="#fn:432">432</a><a class="footnote-ref" id="fnref:433" href="#fn:433">433</a><a class="footnote-ref" id="fnref:434" href="#fn:434">434</a> The patent was filed by VSSC in 2005 and was granted in 2012.</li>
<li>Single-crystalline Scandium Nitride, that has the ability to convert infrared light into energy, Scientists based in Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bengaluru have discovered a novel material that can emit, detect, and modulate infrared light with high efficiency making it useful for solar and thermal energy harvesting and for optical communication devices.<a class="footnote-ref" id="fnref:435" href="#fn:435">435</a><a class="footnote-ref" id="fnref:436" href="#fn:436">436</a></li>
<li>Low-threshold gain lasers, researchers from IISER, Bhopal have made a breakthrough in field of low threshold gain lasers using crystals of cesium lead bromide they are able to produce high-intensity lasers with very low energy output.<a class="footnote-ref" id="fnref:437" href="#fn:437">437</a></li>
<li><a href="/facts/Indian_Ocean_Dipole/FVupAaA3">Indian Ocean Dipole</a> is an unusual pattern in the ocean-atmosphere system of the equatorial Indian Ocean that influences the monsoon and can offset the adverse impact of El Nino. It is typically characterized by cooler than normal eastern equatorial Indian Ocean and warmer than normal west and unusual equatorial easterly winds. It was discovered in Centre for Atmospheric And Oceanic Sciences, <a href="/facts/Indian_Institute_of_Science/GNxvFXWn">IISc.</a> team led by NH Saji in 1999.<a class="footnote-ref" id="fnref:438" href="#fn:438">438</a></li>
<li><a href="/facts/Iron/DkICCKIC">Iron</a> <a href="/facts/Ion/wrbwhF3z">Ion</a> <a href="/facts/Electric_battery/bqEpm4ue">battery</a>,In 2019 world's 1st iron-ion battery was first invented by team of researchers in IIT Madras.<a class="footnote-ref" id="fnref:439" href="#fn:439">439</a></li>
<li>Solution combustion synthesis (SCS) was accidentally discovered in 1988 at Indian Institute of Science (IISc), Bengaluru, India. SCS involves an exothermic redox chemical reaction between an oxidizer like metal nitrate and a fuel in an aqueous medium.<a class="footnote-ref" id="fnref:440" href="#fn:440">440</a></li>
<li><a href="/facts/Defluoridation/75QqRvWs">Nalgonda Technique</a> is a technique for defluoridation to reduce the fluoride levels in water developed by <a href="/facts/National_Environmental_Engineering_Research_Institute/IYVGB8bI">National Environmental Engineering Research Institute</a>, Nagpur.<a class="footnote-ref" id="fnref:441" href="#fn:441">441</a><a class="footnote-ref" id="fnref:442" href="#fn:442">442</a></li>
<li>Electrically Excited Synchronous Motor (EESM) or Rare earth free motor: In 2021 deep-tech startup Chara Technologies has built scalable, cloud-controlled electric vehicle motors free of toxic rare-earth metals, thus cutting a massive dependency on imports to accelerate electric mobility in India.<a class="footnote-ref" id="fnref:443" href="#fn:443">443</a><a class="footnote-ref" id="fnref:444" href="#fn:444">444</a></li>
<li><a href="/facts/Methanol_fuel/M57QVf9k">MD-15</a> is a new methanol fuel grade in which Methanol is blended with diesel. Research Design and Standards Organisation (RDSO), in collaboration with the Indian Oil Corporation Ltd (IOCL), has developed a special cost-effective fuel that would not only minimize IR's dependency on diesel, but will also be emit fewer pollutants. IOCL developed the composition, adding 14% additives (developed indigenously by IOCL) along with 71% mineral diesel, 15% methanol. MD-15 fuelled engine has shown superior performance, emission and combustion characteristics than the mineral diesel fuelled engine.<a class="footnote-ref" id="fnref:445" href="#fn:445">445</a><a class="footnote-ref" id="fnref:446" href="#fn:446">446</a></li>
<li><a href="/facts/Photon_Multiplicity_Detector/eFkJN1Rr">Photon Multiplicity Detector</a>, is a detector for study of <a href="/facts/Quark-gluon_plasma/TQ8RPydR">Quark-gluon plasma</a> and <a href="/facts/Photons/mFNhAEzA">photons</a> developed by <a href="/facts/Institute_of_Physics%2c_Bhubaneswar/wLFUX4ov">Institute of Physics</a> and <a href="/facts/Variable_Energy_Cyclotron_Centre/mqQD02yw">Variable Energy Cyclotron Centre</a>, PMD is used in <a href="/facts/Large_Hadron_Collider/XWJCFSqT">Large Hadron Collider</a> to measure the multiplicity of photons.<a class="footnote-ref" id="fnref:447" href="#fn:447">447</a><a class="footnote-ref" id="fnref:448" href="#fn:448">448</a><a class="footnote-ref" id="fnref:449" href="#fn:449">449</a></li>
<li>Phytorid Wastewater Treatment Technology, is a solution for sustainable wastewater treatment, developed by NEERI (CSIR), It is particularly useful for regions lacking advanced sewage infrastructure.<a class="footnote-ref" id="fnref:450" href="#fn:450">450</a><a class="footnote-ref" id="fnref:451" href="#fn:451">451</a></li>
<li><a href="/facts/Unified_Payments_Interface/hfwNqIYx">Unified Payments Interface</a> – An instant real-time bank to bank <a href="/facts/Internet_Protocol/Qq6VeEal">payments protocol</a> system developed by National Payments Corporation of India (NPCI) facilitated by QR code and Virtual Private Address(VPA) or UPI ID. UPI has able to make India a cashless and cardless economy, also strain on ATM infrastructure has reduced significantly.</li>
<li><a href="/facts/Digital_rupee/I0gVbqmM">Digital rupee</a> (e₹) or eINR or e-rupee is a world's first digital national currency, to be issued by the Reserve Bank of India (RBI) as a central bank digital currency (CBDC). Digital Rupee is using blockchain distributed-ledger technology. Digital rupee users to hit 50,000 by Jan-end on better acceptance.<a class="footnote-ref" id="fnref:452" href="#fn:452">452</a></li></ul>
<h3>Weapon systems</h3>
<ul><li><a href="/facts/Advanced_Towed_Artillery_Gun_System/UzYEP2bh">ATAGS</a> – Bharat Forge and the DRDO has developed world's first electric artillery gun<a class="footnote-ref" id="fnref:453" href="#fn:453">453</a></li>
<li>Bhargavastra, is the world's first kind of multi-micro-missile system to counter swarm drones, low-cost portable system developed by Solar Defence and Aerospace.<a class="footnote-ref" id="fnref:454" href="#fn:454">454</a><a class="footnote-ref" id="fnref:455" href="#fn:455">455</a></li>
<li><a href="/facts/Combat_helmet/KTKnjrMd">Rifle-rated ballistic helmet</a>, <a href="/facts/MKU_(company)/WpE1YJSA">MKU</a> has developed what it bills as "a first-of-its-kind rifle-rated ballistic helmet", MKU states that the Kavro Doma 360 is "the first anti-rifle helmet in the world that does not have bolts or any metal parts"<a class="footnote-ref" id="fnref:456" href="#fn:456">456</a></li>
<li>Critical Situation Response Vehicle (CSRV) – The Central Reserve Police Force (CRPF) has made and inducted a bomb/bulletproof armoured vehicle. The latest all-terrain highly sophisticated vehicle 'CSRV' has given a shot in the arm to the Central Reserve Police Force engaged in counter-terror operations.</li>
<li>E-bomb – The Defence Research and Development Organisation (DRDO) has been developing an e-bomb which will emit electromagnetic shock waves that destroy electronic circuits and communication networks of enemy force.<a class="footnote-ref" id="fnref:457" href="#fn:457">457</a> The tow bodies in Lakshya-2 Weapon Delivery Configuration carry High Energy Weapon Payload.<a class="footnote-ref" id="fnref:458" href="#fn:458">458</a></li>
<li>Phosphoric Acid Fuel Cell air-independent propulsion (PAFC AIP) is a 270 kilowatt phosphoric acid fuel cell (PAFC) air-independent propulsion (AIP) system to power the Kalvari-class submarines is developed by the <a href="/facts/Naval_Materials_Research_Laboratory/kTMGxfsm">Naval Materials Research Laboratory</a> of Indian Defence Research and Development Organisation in collaboration with <a href="/facts/Larsen_%2526_Toubro/cFswBIV8">Larsen & Toubro</a> and <a href="/facts/Thermax/hvvSp3H1">Thermax</a>. The patent is owned by <a href="/facts/DRDO/HYTLS49D">DRDO</a>. Its application is considered to be wide and it can also power ships in future.<a class="footnote-ref" id="fnref:459" href="#fn:459">459</a></li></ul>
<h3>Automotive innovations</h3>
<ul><li><a href="/facts/Man_Mohan_Suri/wywz5lQ9">Suri Transmission</a>, is a hydromechanical transmission unit for diesel locomotives developed by Man Mohan Suri.</li>
<li><a href="/facts/Air_conditioning/bK2sIKQd">Helmet AC</a> - Featuring a plastic top and built-in-fan-like structure, the AC helmets are powered by a battery pack, which is worn by the traffic police officials on their waist. These helmets work for around 8 hours on a single full charge.<a class="footnote-ref" id="fnref:460" href="#fn:460">460</a></li>
<li><a href="/facts/CNG/tMsYjxMK">CNG</a> car/vehicle – <a href="/facts/Bajaj_Auto/F7QqEDBm">Bajaj Auto</a> launched the first 'commercial' lot of its CNG (Compressed Natural Gas) autorickshaws in Delhi on 29 May 2000.By 1 December 2002, the last diesel bus had disappeared from Delhi's roads, all buses were running on CNG.At the beginning of 2005, 10,300 CNG busses, 10,000 CNG taxis and 10,000 CNG cars run on Delhi's roads.<a class="footnote-ref" id="fnref:461" href="#fn:461">461</a></li></ul>
<h3>Mathematics</h3>
See also: <a href="/facts/Indian_mathematics/l9f6ke00">Indian mathematics</a>
<ul><li><a href="/facts/AKS_primality_test/VRkvQVeT">AKS primality test</a> and <a href="/facts/Agrawal%2527s_conjecture/WzpQszey">Agrawal's conjecture</a>– The AKS primality test is a <a href="/facts/Deterministic_algorithm/v8x4wz35">deterministic</a> <a href="/facts/Primality_test/dLMr8E0u">primality-proving</a> <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> created and published by three <a href="/facts/Indian_Institute_of_Technology_Kanpur/Xr7t3nfR">Indian Institute of Technology Kanpur</a> computer scientists, <a href="/facts/Manindra_Agrawal/WTYrlgIx">Manindra Agrawal</a>, <a href="/facts/Neeraj_Kayal/x1Mw7QBy">Neeraj Kayal</a>, and <a href="/facts/Nitin_Saxena/96BsxRxR">Nitin Saxena</a> on 6 August 2002 in a paper titled <a href="http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf">PRIMES is in P</a>.<a class="footnote-ref" id="fnref:462" href="#fn:462">462</a><a class="footnote-ref" id="fnref:463" href="#fn:463">463</a> Commenting on the impact of this discovery, <a href="/facts/Paul_Leyland/hptCpdeT">Paul Leyland</a> noted: "One reason for the excitement within the mathematical community is not only does this algorithm settle a long-standing problem, it also does so in a brilliantly simple manner. Everyone is now wondering what else has been similarly overlooked".<a class="footnote-ref" id="fnref:464" href="#fn:464">464</a><a class="footnote-ref" id="fnref:465" href="#fn:465">465</a></li>
<li><a href="/facts/Block_design/R523MRYh">Partial Balanced Incomplete Block Designs (BIBD)</a> was developed by <a href="/facts/Raj_Chandra_Bose/RI0WHXIV">Raj Chandra Bose</a> and Kesavan Raghavan Nair in 1939.<a class="footnote-ref" id="fnref:466" href="#fn:466">466</a></li>
<li><a href="/facts/Multivariate_statistics/tDuNcWrL">Multivariate Statistical Theory</a>, is one of the base foundational concept of statistics was developed by <a href="/facts/C._R._Rao/SxnbA5YV">C. R. Rao</a> in 1952 when he was in <a href="/facts/Indian_Statistical_Institute/T0wB4jUX">Indian Statistical Institute</a>, Kolkata.</li>
<li><a href="/facts/Score_test/paM5A8pV">Rao's Score Test</a> was first published in 1948 in Sankhya: The Indian Journal of Statistics titled On Distributions of the Maximum Likelihood Estimates by <a href="/facts/C._R._Rao/SxnbA5YV">C. R. Rao</a>.<a class="footnote-ref" id="fnref:467" href="#fn:467">467</a></li>
<li><a href="/facts/Samarendra_Nath_Roy/fX9ndjg1">Roy’s Largest Root Test</a>, proposed the test in 1953 as part of his "union-intersection principle", a unified approach to multivariate hypothesis testing.<a class="footnote-ref" id="fnref:468" href="#fn:468">468</a></li>
<li><a href="/facts/Samarendra_Nath_Roy/fX9ndjg1">Roy-Hotelling Theorem</a>, is used to connects the eigenvalues of matrices in multivariate statistics proposed in 1953.<a class="footnote-ref" id="fnref:469" href="#fn:469">469</a></li>
<li><a href="/facts/Seshadri_constant/h22lBMP0">Seshadri constant</a> – In <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>, a Seshadri constant is an invariant of an ample line bundle L at a point P on an <a href="/facts/Algebraic_variety/Vk7f97vn">algebraic variety</a>.The name is in honour of the Indian mathematician <a href="/facts/C._S._Seshadri/YIrFP80W">C. S. Seshadri</a>.</li>
<li><a href="/facts/Basu%2527s_theorem/LlmmXdHH">Basu's theorem</a> – The Basu's theorem, a result of <a href="/facts/Debabrata_Basu/Agx5Sk1V">Debabrata Basu</a> (1955) states that any complete sufficient statistic is independent of any ancillary statistic.<a class="footnote-ref" id="fnref:470" href="#fn:470">470</a><a class="footnote-ref" id="fnref:471" href="#fn:471">471</a></li>
<li><a href="/facts/Kosambi%25E2%2580%2593Karhunen%25E2%2580%2593Lo%25C3%25A8ve_theorem/HX3cIv6g">Kosambi–Karhunen–Loève theorem</a> (also known as the <a href="/facts/Karhunen%25E2%2580%2593Lo%25C3%25A8ve_theorem/HX3cIv6g">Karhunen–Loève theorem</a>) The Kosambi-Karhunen-Loève theorem is a representation of a stochastic process as an infinite linear combination of <a href="/facts/Orthogonal_function/2MmN826Q">orthogonal functions</a>, analogous to a <a href="/facts/Fourier_series/s3fsxPAT">Fourier series</a> representation of a function on a bounded interval. Stochastic processes given by infinite series of this form were first<a class="footnote-ref" id="fnref:472" href="#fn:472">472</a> considered by <a href="/facts/Damodar_Dharmananda_Kosambi/CwdtA5Jz">Damodar Dharmananda Kosambi</a>.<a class="footnote-ref" id="fnref:473" href="#fn:473">473</a></li>
<li><a href="/facts/Dattaraya_Ramchandra_Kaprekar/Hhp1g2S4">Kaprekar Constants</a>: Numbers 495 and 6174. The Indian mathematician <a href="/facts/Dattaraya_Ramchandra_Kaprekar/Hhp1g2S4">D.R.Kaprekar</a> discovered the number 6174 is reached after repeatedly subtracting the smallest number from the largest number that can be formed from any four digits not all the same. The number 495 is similarly reached for three digits number.</li>
<li><a href="/facts/Kosaraju%2527s_algorithm/MYLcDEc0">Kosaraju's algorithm</a> is a linear time algorithm to find the strongly connected components of a directed graph. Aho, Hopcroft and Ullman credit it to S. Rao Kosaraju and Micha Sharir. Kosaraju suggested it in 1978.</li>
<li><a href="/facts/Ramanujan_theta_function/Hz3vaAED">Ramanujan theta function</a>, <a href="/facts/Ramanujan_prime/Ygp43e73">Ramanujan prime</a>, <a href="/facts/Ramanujan_summation/3GNBWCoB">Ramanujan summation</a>, <a href="/facts/Ramanujan_graph/T0lXTlmW">Ramanujan graph</a> and <a href="/facts/Ramanujan%2527s_sum/4xCStJrU">Ramanujan's sum</a> – Discovered by the Indian mathematician <a href="/facts/Srinivasa_Ramanujan/HBPr4bzd">Srinivasa Ramanujan</a> in the early 20th century.<a class="footnote-ref" id="fnref:474" href="#fn:474">474</a></li>
<li><a href="/facts/Shrikhande_graph/NVH1YV71">Shrikhande graph</a> – <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">Graph</a> invented by the Indian mathematician <a href="/facts/S.S._Shrikhande/hnRScWY1">S.S. Shrikhande</a> in 1959.</li></ul>
<h3>Sciences</h3>
 
<ul><li><a href="/facts/Ammonium_nitrite/rQPINDhV">Ammonium nitrite, synthesis in pure form</a> – <a href="/facts/Prafulla_Chandra_Roy/PfWsWeka">Prafulla Chandra Roy</a> synthesised NH4NO2 in its pure form, and became the first scientist to have done so.<a class="footnote-ref" id="fnref:475" href="#fn:475">475</a> Prior to Ray's synthesis of Ammonium nitrite it was thought that the compound undergoes rapid thermal decomposition releasing nitrogen and water in the process.<a class="footnote-ref" id="fnref:476" href="#fn:476">476</a></li>
<li>Bhatnagar-Mathur Magnetic Interference Balance: Invented jointly by <a href="/facts/Shanti_Swarup_Bhatnagar/hBIP9YPz">Shanti Swarup Bhatnagar</a> and K.N. Mathur in 1928, the so-called 'Bhatnagar-Mathur Magnetic Interference Balance' was a modern instrument used for measuring various magnetic properties.<a class="footnote-ref" id="fnref:477" href="#fn:477">477</a> The first appearance of this instrument in Europe was at a <a href="/facts/Royal_Society/KI5yXCuV">Royal Society</a> exhibition in London, where it was later marketed by British firm Messers Adam Hilger and Co, London.<a class="footnote-ref" id="fnref:478" href="#fn:478">478</a></li>
<li><a href="/facts/Bhabha_scattering/hdTD5ESz">Bhabha scattering</a> – In 1935, Indian nuclear physicist <a href="/facts/Homi_J._Bhabha/hVevadtA">Homi J. Bhabha</a> published a paper in the <a href="/facts/Proceedings_of_the_Royal_Society_A%3a_Mathematical%2c_Physical_and_Engineering_Sciences/qyn2m2ja">Proceedings of the Royal Society, Series A</a>, in which he performed the first calculation to determine the cross section of electron-positron scattering.<a class="footnote-ref" id="fnref:479" href="#fn:479">479</a> Electron-positron scattering was later named Bhabha scattering, in honour of his contributions in the field.<a class="footnote-ref" id="fnref:480" href="#fn:480">480</a></li>
<li><a href="/facts/Bose%25E2%2580%2593Einstein_statistics/Utb2jN3n">Bose–Einstein statistics</a>, <a href="/facts/Bose%25E2%2580%2593Einstein_condensate/76peCwfW">condensate</a> – On 4 June 1924 the Indian physicist <a href="/facts/Satyendra_Nath_Bose/rC6y84HS">Satyendra Nath Bose</a> mailed a short manuscript to <a href="/facts/Albert_Einstein/CNTet8qu">Albert Einstein</a> entitled <a href="http://www.ias.ac.in/jarch/jaa/15/3-7.pdf">Planck's Law and the Light Quantum Hypothesis</a> seeking Einstein's influence to get it published after it was rejected by the prestigious journal <a href="/facts/Philosophical_Magazine/yeTXVoYt">Philosophical Magazine</a>.<a class="footnote-ref" id="fnref:481" href="#fn:481">481</a> The paper introduced what is today called Bose statistics, which showed how it could be used to derive the Planck blackbody spectrum from the assumption that light was made of <a href="/facts/Photons/mFNhAEzA">photons</a>.<a class="footnote-ref" id="fnref:482" href="#fn:482">482</a><a class="footnote-ref" id="fnref:483" href="#fn:483">483</a> Einstein, recognizing the importance of the paper translated it into German himself and submitted it on Bose's behalf to the prestigious <a href="/facts/Zeitschrift_f%25C3%25BCr_Physik/B0VsWLSC">Zeitschrift für Physik</a>.<a class="footnote-ref" id="fnref:484" href="#fn:484">484</a><a class="footnote-ref" id="fnref:485" href="#fn:485">485</a> Einstein later applied Bose's principles on particles with mass and quickly predicted the Bose-Einstein condensate.<a class="footnote-ref" id="fnref:486" href="#fn:486">486</a><a class="footnote-ref" id="fnref:487" href="#fn:487">487</a></li>
<li><a href="/facts/Braunstein-Ghosh-Severini_Entropy/UXmcuj5u">Braunstein-Ghosh-Severini Entropy</a> – This modelling of entropy using network theory is used in the analysis of <a href="/facts/Quantum_gravity/t7whBMNE">quantum gravity</a> and is named after Sibasish Ghosh and his teammates, <a href="/facts/Samuel_L._Braunstein/RQlUKJwj">Samuel L. Braunstein</a> and Simone Severini.</li>
<li><a href="/facts/Dual-phase_steel/IV8I9aTS">Dual-phase steel</a>, was publicly first described in "Microstructure and tensile properties of high strength duplex ferrite–martensite (DFM) steels" by P.C. Chakraborti and M.K. Mitra.<a class="footnote-ref" id="fnref:488" href="#fn:488">488</a></li>
<li><a href="/facts/Galena/eSaK62FA">Galena, applied use in electronics of</a> – Bengali scientist Sir <a href="/facts/Jagadish_Chandra_Bose/r2W5xbXS">Jagadish Chandra Bose</a> effectively used Galena crystals for constructing radio receivers.<a class="footnote-ref" id="fnref:489" href="#fn:489">489</a> The Galena receivers of Bose were used to receive signals consisting of <a href="/facts/Shortwave/7cIaClcB">shortwave</a>, <a href="/facts/Electromagnetic_spectrum/24LARvFY">white light</a> and <a href="/facts/Ultraviolet_light/kncBUqn5">ultraviolet light</a>.<a class="footnote-ref" id="fnref:490" href="#fn:490">490</a> In 1904 Bose patented the use of Galena Detector which he called Point Contact Diode using Galena.<a class="footnote-ref" id="fnref:491" href="#fn:491">491</a></li>
<li><a href="/facts/Mahalanobis_distance/UneEsDng">Mahalanobis distance</a> – Introduced in 1936 by the Indian (Bengali) statistician <a href="/facts/Prasanta_Chandra_Mahalanobis/Xt9ju64V">Prasanta Chandra Mahalanobis</a> (29 June 1893 – 28 June 1972), this distance measure, based upon the correlation between variables, is used to identify and analyze differing pattern with respect to one base.<a class="footnote-ref" id="fnref:492" href="#fn:492">492</a></li>
<li><a href="/facts/Nitrite/qkz2XScK">Mercurous nitrite</a> – The compound mercurous nitrite was discovered in 1896 by the Bengali chemist Prafulla Chandra Roy, who published his findings in the <a href="/facts/Asiatic_Society/J3k2MWAz">Journal of the Asiatic Society of Bengal</a>.<a class="footnote-ref" id="fnref:493" href="#fn:493">493</a> The discovery contributed as a base for significant future research in the field of chemistry.<a class="footnote-ref" id="fnref:494" href="#fn:494">494</a></li>
<li><a href="/facts/Ramachandran_plot/0KVStzpJ">Ramachandran plot</a>, Ramachandran map, and Ramachandran angles: The Ramachandran plot and Ramachandran map were developed by <a href="/facts/Gopalasamudram_Narayana_Iyer_Ramachandran/vfRYU9zj">Gopalasamudram Narayana Iyer Ramachandran</a>, who published his results in the <a href="/facts/Journal_of_Molecular_Biology/0tFTy8vw">Journal of Molecular Biology</a> in 1963. He also developed the Ramachandran angles, which serve as a convenient tool for <a href="/facts/Communication/EGEkchsT">communication</a>, representation, and various kinds of <a href="/facts/Data_analysis/CNtARxLW">data analysis</a>.<a class="footnote-ref" id="fnref:495" href="#fn:495">495</a></li>
<li><a href="/facts/Raman_effect/obhSpgrR">Raman effect</a> – The Encyclopædia Britannica (2008) reports: "change in the wavelength of light that occurs when a light beam is deflected by molecules. The phenomenon is named for <a href="/facts/Sir_Chandrasekhara_Venkata_Raman/UBjLvevH">Sir Chandrasekhara Venkata Raman</a>, who discovered it in 1928. When a beam of light traverses a dust-free, transparent sample of a chemical compound, a small fraction of the light emerges in directions other than that of the incident (incoming) beam. Most of this scattered light is of unchanged wavelength. A small part, however, has wavelengths different from that of the incident light; its presence is a result of the Raman effect."<a class="footnote-ref" id="fnref:496" href="#fn:496">496</a></li>
<li><a href="/facts/Raychaudhuri_equation/1zLwlUjX">Raychaudhuri equation</a> – Discovered by the <a href="/facts/Bengali_people/zUbaEVXE">Bengali</a> physicist <a href="/facts/Amal_Kumar_Raychaudhuri/sB2PznW9">Amal Kumar Raychaudhuri</a> in 1954. This was a key ingredient of the <a href="/facts/Penrose-Hawking_singularity_theorems/5wD1VGf7">Penrose-Hawking singularity theorems</a> of <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>.<a class="footnote-ref" id="fnref:497" href="#fn:497">497</a></li>
<li><a href="/facts/Saha_ionization_equation/AoapeRzM">Saha ionization equation</a> is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure.</li>
<li>Periodicity in Nuclear Properties: A sharp pattern is discovered by an Indian researcher regarding the nuclear properties of chemical elements. The remarkable deviations are noticed near the magic numbers.<a class="footnote-ref" id="fnref:498" href="#fn:498">498</a></li>
<li>Process of formation of the E layer of the ionosphere and night sky luminiscence: Discovered by the Indian physicist, Sisir Kumar Mitra.<a class="footnote-ref" id="fnref:499" href="#fn:499">499</a></li>
<li><a href="/facts/Boson/XtPFcjb5">Boson</a>: Satyendra Nath Bose's research led to the discovery of the <a href="/facts/Boson/XtPFcjb5">Boson</a>, one of the <a href="/facts/Elementary_particles/CTFDM97U">elementary particles</a> on the <a href="/facts/Standard_Model/LhVGf9ow">Standard Model</a> of <a href="/facts/Particle_Physics/YgIuyj2t">Particle Physics</a>.</li></ul>
<h3>Space</h3>

<ul><li><a href="/facts/Lunar_water/TKfE5qLU">Lunar water</a> – Although the presence of water ice on the Moon has been conjectured by various scientists since the 1960s, inconclusive evidence of free water ice had also been identified. The first incontrovertible evidence of water on the Moon was provided by the payload Chace carried by the <a href="/facts/Moon_Impact_Probe/HuzJUmqL">Moon Impact Probe</a> released by <a href="/facts/Chandrayaan-1/IqP3zwxy">Chandrayaan-1</a> in 2009,<a class="footnote-ref" id="fnref:500" href="#fn:500">500</a><a class="footnote-ref" id="fnref:501" href="#fn:501">501</a><a class="footnote-ref" id="fnref:502" href="#fn:502">502</a> confirmed and established by <a href="/facts/NASA/TIMCV0yV">NASA</a>.<a class="footnote-ref" id="fnref:503" href="#fn:503">503</a></li>
<li><a href="/facts/Saha_ionisation_equation/AoapeRzM">Saha ionisation equation</a> – The Saha equation, derived by the Bengali scientist <a href="/facts/Meghnad_Saha/uJDVzRVo">Meghnad Saha</a> (6 October 1893 – 16 February 1956) in 1920, conceptualises <a href="/facts/Ionisation/W13Ceavd">ionisations</a> in context of stellar atmospheres.<a class="footnote-ref" id="fnref:504" href="#fn:504">504</a></li>
<li><a href="/facts/Quasi-normal_mode/a9eTqzNR">Quasi-normal modes</a> of <a href="/facts/Black_holes/1r2lmkcF">black holes</a> – <a href="/facts/C._V._Vishveshwara/IoEubMnK">C. V. Vishveshwara</a> discovered the <a href="/facts/Quasi-normal_mode/a9eTqzNR">quasi-normal modes</a> of black holes.<a class="footnote-ref" id="fnref:505" href="#fn:505">505</a> These modes of black hole vibrations are one of the main targets of observation using the gravitational wave detector.</li>
<li><a href="/facts/Chandrasekhar_limit/KojyANXK">Chandrasekhar limit</a>: <a href="/facts/Subramanyan_Chandrasekhar/LQID778M">Subramanyan Chandrasekhar</a> discovered the maximum mass of a stable <a href="/facts/White_dwarf/gIYlTtrC">white dwarf</a> star.</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Timeline_of_Indian_innovation/v7UrKG1y">Timeline of Indian innovation</a></li>
<li><a href="/facts/History_of_science_and_technology_in_India/BhwzGDTn">History of science and technology in India</a></li>
<li><a href="/facts/Timeline_of_historic_inventions/Wsa2pNfV">Timeline of historic inventions</a></li>
<li><a href="/facts/List_of_Indian_mathematicians/ushvFSAf">List of Indian mathematicians</a></li>
<li><a href="/facts/List_of_Indian_scientists/HfXhHJY8">List of Indian scientists</a></li>
<li>List of Indian physicists</li></ul>
<h2 id="notes">Notes</h2>

<h2 id="bibliography">Bibliography</h2>

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<li><a href="/facts/T.A._Sarasvati_Amma/KSLr4Dpt">Amma, T. A. Sarasvati</a> (1999) [1979]. Geometry in Ancient and Medieval India. Delhi: Motilal Banarsidass Publication. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 81-208-1344-8.</li>
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<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.themysteriousindia.net/ancient-india-inventions-science-technology/">Ancient India's Inventions In Science And Technology</a></li>
<li><a href="http://www.indianscience.org/essays/essays.shtml">Essays on Indian Science and Technology.</a></li>
<li><a href="https://web.archive.org/web/20140224120624/http://www.sciencecongress.nic.in/html/pdf/e-book/oct-nov-2012.pdf">P. K. Ray, SCIENCE, CULTURE AND DEVELOPMENT – A CONNECTED PHENOMENA, Everyman's Science Vol.</a></li>
<li>History of Science in South Asia (<a href="http://hssa-journal.org">hssa-journal.org</a>). HSSA is a peer-reviewed, open-access, online journal for the history of science in India.</li></ul>

<h2 id="references">References</h2>

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<li id="fn:2">Kriger & Connah (2006), page 120 <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Kriger & Connah (2006), page 120 <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Kriger & Connah (2006), page 120 <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Encyclopædia Britannica (2008). jute. <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
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<li id="fn:11">Book Two of Dioscorides' Materia Medica. The book is downloadable from links at the Wikipedia Dioscorides page. <a href="/wiki/Dioscorides" target="_blank">/wiki/Dioscorides</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">"de materia medica" – via Internet Archive. <a href="http://archive.org/details/de-materia-medica" target="_blank">http://archive.org/details/de-materia-medica</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Kieschnick (2003) <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Kieschnick (2003), page 258 <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">Kieschnick (2003), page 258 <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">Livingston & Beach, 19 <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
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<li id="fn:18">Encyclopædia Britannica (2008). Pagoda. <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
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<li id="fn:21">Asher 2015, pp. 1–5. - Asher, Frederick M. (2015). Nalanda: Situating the Great Monastery. Marga. ISBN 978-93-83243-07-5. <a href="https://books.google.com/books?id=oRCVrgEACAAJ" target="_blank">https://books.google.com/books?id=oRCVrgEACAAJ</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">Kumar (2018). - Kumar, Pintu (2018). Buddhist Learning in South Asia: Education, Religion, and Culture at the Ancient Sri Nalanda Mahavihara. Lexington Books. <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">"History | District Nalanda, Government of Bihar | India". nalanda.nic.in. 15 June 2023. Retrieved 2 June 2023. <a href="https://nalanda.nic.in/en/history/" target="_blank">https://nalanda.nic.in/en/history/</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
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<li id="fn:25">Pinkney 2015, pp. 111–149. - Pinkney, Andrea Marion (1 July 2015). "Looking West to India: Asian education, intra-Asian renaissance, and the Nalanda revival". Modern Asian Studies. 49 (1): 111–149. doi:10.1017/S0026749X13000310. S2CID 144865654. <a href="https://doi.org/10.1017%2FS0026749X13000310" target="_blank">https://doi.org/10.1017%2FS0026749X13000310</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
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<li id="fn:28">Cassell, Hartwig; Helms, Hermann (28 May 1916). "American Chess Bulletin". H. Cassell and H. Helms. – via Google Books. <a href="https://books.google.com/books?id=CqJJAAAAYAAJ&dq=brahmajala+sutta+games&pg=RA2-PA104" target="_blank">https://books.google.com/books?id=CqJJAAAAYAAJ&dq=brahmajala+sutta+games&pg=RA2-PA104</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></li>
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<li id="fn:30">"All India Carrom Federation". Archived from the original on 16 February 2015. Retrieved 2 February 2015. <a href="https://web.archive.org/web/20150216055759/http://indiancarrom.com/brief-of-the-game.htm" target="_blank">https://web.archive.org/web/20150216055759/http://indiancarrom.com/brief-of-the-game.htm</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></li>
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<li id="fn:32">Murray (1913) <a href="#fnref:32" class="footnote-back-ref">↩</a></li>
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<li id="fn:41">Meri (2005), page 148 <a href="#fnref:41" class="footnote-back-ref">↩</a></li>
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<li id="fn:43">Encyclopædia Britannica (2002). Chess: Ancient precursors and related games. <a href="#fnref:43" class="footnote-back-ref">↩</a></li>
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<li id="fn:49">Alter, page 88 <a href="#fnref:49" class="footnote-back-ref">↩</a></li>
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<li id="fn:74">Encyclopædia Britannica (2008). calico <a href="#fnref:74" class="footnote-back-ref">↩</a></li>
<li id="fn:75">Encyclopædia Britannica (2008). calico <a href="#fnref:75" class="footnote-back-ref">↩</a></li>
<li id="fn:76">Encyclopædia Britannica (2008). calico <a href="#fnref:76" class="footnote-back-ref">↩</a></li>
<li id="fn:77">Encyclopædia Britannica (2008). calico <a href="#fnref:77" class="footnote-back-ref">↩</a></li>
<li id="fn:78">Baber (1996), page 57 <a href="#fnref:78" class="footnote-back-ref">↩</a></li>
<li id="fn:79">Baber (1996), page 57 <a href="#fnref:79" class="footnote-back-ref">↩</a></li>
<li id="fn:80">Baber (1996), page 57 <a href="#fnref:80" class="footnote-back-ref">↩</a></li>
<li id="fn:81">Encyclopædia Britannica (2008). cashmere. <a href="#fnref:81" class="footnote-back-ref">↩</a></li>
<li id="fn:82">Encyclopædia Britannica (2008). kashmir shawl. <a href="#fnref:82" class="footnote-back-ref">↩</a></li>
<li id="fn:83">Smith, C. Wayne; Cothren, J. Tom (1999). Cotton: Origin, History, Technology, and Production. Vol. 4. John Wiley & Sons. pp. viii. ISBN 978-0471180456. The first improvement in spinning technology was the spinning wheel, which was invented in India between 500 and 1000 A.D. <a href="978-0471180456" target="_blank">978-0471180456</a> <a href="#fnref:83" class="footnote-back-ref">↩</a></li>
<li id="fn:84">Encyclopædia Britannica (2008). chintz <a href="#fnref:84" class="footnote-back-ref">↩</a></li>
<li id="fn:85">Encyclopædia Britannica (2008). chintz <a href="#fnref:85" class="footnote-back-ref">↩</a></li>
<li id="fn:86">Hāṇḍā (1998), page 133 <a href="#fnref:86" class="footnote-back-ref">↩</a></li>
<li id="fn:87">Stein (1998), page 47 <a href="#fnref:87" class="footnote-back-ref">↩</a></li>
<li id="fn:88">Wisseman & Williams (1994), page 127 <a href="#fnref:88" class="footnote-back-ref">↩</a></li>
<li id="fn:89">The Columbia Encyclopedia, Sixth Edition. cotton. <a href="#fnref:89" class="footnote-back-ref">↩</a></li>
<li id="fn:90">Angela Lakwete: Inventing the Cotton Gin: Machine and Myth in Antebellum America, The Johns Hopkins University Press, 2003, ISBN 0-8018-7394-0, p. 5 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:90" class="footnote-back-ref">↩</a></li>
<li id="fn:91">Baber (1996), page 56 <a href="#fnref:91" class="footnote-back-ref">↩</a></li>
<li id="fn:92">Baber (1996), page 57 <a href="#fnref:92" class="footnote-back-ref">↩</a></li>
<li id="fn:93">Irfan Habib, Economic History of Medieval India, 1200–1500, page 53, Pearson Education <a href="/wiki/Irfan_Habib" target="_blank">/wiki/Irfan_Habib</a> <a href="#fnref:93" class="footnote-back-ref">↩</a></li>
<li id="fn:94">Irfan Habib (2011), Economic History of Medieval India, 1200–1500, pp. 53–54, Pearson Education <a href="/wiki/Irfan_Habib" target="_blank">/wiki/Irfan_Habib</a> <a href="#fnref:94" class="footnote-back-ref">↩</a></li>
<li id="fn:95">Encyclopædia Britannica (2008). interior design <a href="#fnref:95" class="footnote-back-ref">↩</a></li>
<li id="fn:96">Encyclopædia Britannica (2008). crewel work <a href="#fnref:96" class="footnote-back-ref">↩</a></li>
<li id="fn:97">Encyclopædia Britannica (2008). quilting <a href="#fnref:97" class="footnote-back-ref">↩</a></li>
<li id="fn:98">Encyclopædia Britannica (2008). crewel work <a href="#fnref:98" class="footnote-back-ref">↩</a></li>
<li id="fn:99">Encyclopædia Britannica (2008). quilting <a href="#fnref:99" class="footnote-back-ref">↩</a></li>
<li id="fn:100">Barker, page 13 <a href="#fnref:100" class="footnote-back-ref">↩</a></li>
<li id="fn:101">Barker, page 13 <a href="#fnref:101" class="footnote-back-ref">↩</a></li>
<li id="fn:102">Beer, page 60 <a href="#fnref:102" class="footnote-back-ref">↩</a></li>
<li id="fn:103">Wise, page 11–12 <a href="#fnref:103" class="footnote-back-ref">↩</a></li>
<li id="fn:104">Wise, page 11–12 <a href="#fnref:104" class="footnote-back-ref">↩</a></li>
<li id="fn:105">Beer, page 60 <a href="#fnref:105" class="footnote-back-ref">↩</a></li>
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<li id="fn:107">Irfan Habib (2011), Economic History of Medieval India, 1200–1500, p. 53, Pearson Education <a href="/wiki/Irfan_Habib" target="_blank">/wiki/Irfan_Habib</a> <a href="#fnref:107" class="footnote-back-ref">↩</a></li>
<li id="fn:108">Todd, Jan (1995). From Milo to Milo: A History of Barbells, Dumbells, and Indian Clubs Archived 31 July 2012 at the Wayback Machine. Accessed in September 2008. Hosted on the LA84 Foundation Sports Library. <a href="http://www.la84foundation.org/SportsLibrary/IGH/IGH0306/IGH0306c.pdf" target="_blank">http://www.la84foundation.org/SportsLibrary/IGH/IGH0306/IGH0306c.pdf</a> <a href="#fnref:108" class="footnote-back-ref">↩</a></li>
<li id="fn:109">Todd, Jan (1995). From Milo to Milo: A History of Barbells, Dumbells, and Indian Clubs Archived 31 July 2012 at the Wayback Machine. Accessed in September 2008. Hosted on the LA84 Foundation Sports Library. <a href="http://www.la84foundation.org/SportsLibrary/IGH/IGH0306/IGH0306c.pdf" target="_blank">http://www.la84foundation.org/SportsLibrary/IGH/IGH0306/IGH0306c.pdf</a> <a href="#fnref:109" class="footnote-back-ref">↩</a></li>
<li id="fn:110">Todd, Jan (1995). From Milo to Milo: A History of Barbells, Dumbells, and Indian Clubs Archived 31 July 2012 at the Wayback Machine. Accessed in September 2008. Hosted on the LA84 Foundation Sports Library. <a href="http://www.la84foundation.org/SportsLibrary/IGH/IGH0306/IGH0306c.pdf" target="_blank">http://www.la84foundation.org/SportsLibrary/IGH/IGH0306/IGH0306c.pdf</a> <a href="#fnref:110" class="footnote-back-ref">↩</a></li>
<li id="fn:111">cā̃po (चाँपो IPA: [tʃãːpoː]) is the imperative of cā̃pnā (चाँपना IPA: [tʃãːpnaː]), "to smear, knead the muscles, massage the head and hair" <a href="/wiki/Help:IPA/Hindi_and_Urdu" target="_blank">/wiki/Help:IPA/Hindi_and_Urdu</a> <a href="#fnref:111" class="footnote-back-ref">↩</a></li>
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<li id="fn:169">For the etching technique, see MacKay, Ernest (1925). "Sumerian Connexions with Ancient India". The Journal of the Royal Asiatic Society of Great Britain and Ireland (4): 699. JSTOR 25220818. <a href="/wiki/JSTOR_(identifier)" target="_blank">/wiki/JSTOR_(identifier)</a> <a href="#fnref:169" class="footnote-back-ref">↩</a></li>
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<li id="fn:171">"Such beads occur fairly largely on all the principal sites of the Harappan civilisation." in Pakistan Archaeology No.2. 1965. p. 21. <a href="https://archive.org/details/in.ernet.dli.2015.532513/page/n49/mode/2up" target="_blank">https://archive.org/details/in.ernet.dli.2015.532513/page/n49/mode/2up</a> <a href="#fnref:171" class="footnote-back-ref">↩</a></li>
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<li id="fn:202">Sherby, Oleg D.; Wadsworth, Jeffrey (November 2001). "Ancient blacksmiths, the Iron Age, Damascus steels, and modern metallurgy". Journal of Materials Processing Technology. 117 (3): 347–353. doi:10.1016/S0924-0136(01)00794-4. OSTI 790393. <a href="https://digital.library.unt.edu/ark:/67531/metadc718386/" target="_blank">https://digital.library.unt.edu/ark:/67531/metadc718386/</a> <a href="#fnref:202" class="footnote-back-ref">↩</a></li>
<li id="fn:203">Ian Strangeways, A History of rain gauges, TerraData, 2010 <a href="#fnref:203" class="footnote-back-ref">↩</a></li>
<li id="fn:204">Kosambi (1982) The Culture and Civilization of Ancient India in Historical Outline, p. 153, ISBN 978-0-7069-1399-6 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:204" class="footnote-back-ref">↩</a></li>
<li id="fn:205">Venable, Shannon L. (2011). Gold: A Cultural Encyclopedia. Santa Barbara, CA: ABC-CLIO, LLC. p. 264. ISBN 978-0313-384318. <a href="978-0313-384318" target="_blank">978-0313-384318</a> <a href="#fnref:205" class="footnote-back-ref">↩</a></li>
<li id="fn:206">Kenoyer, 265 <a href="#fnref:206" class="footnote-back-ref">↩</a></li>
<li id="fn:207">Kenoyer, 265 <a href="#fnref:207" class="footnote-back-ref">↩</a></li>
<li id="fn:208">In the third millennium BCE the Indus measuring system was further developed in the ancient regions of Iran and Afghanistan – Iwata, 2254. <a href="#fnref:208" class="footnote-back-ref">↩</a></li>
<li id="fn:209">Iwata2254 <a href="#fnref:209" class="footnote-back-ref">↩</a></li>
<li id="fn:210">Baber, 23 <a href="#fnref:210" class="footnote-back-ref">↩</a></li>
<li id="fn:211">Iwata2254 <a href="#fnref:211" class="footnote-back-ref">↩</a></li>
<li id="fn:212">In the third millennium BCE the Indus measuring system was further developed in the ancient regions of Iran and Afghanistan – Iwata, 2254. <a href="#fnref:212" class="footnote-back-ref">↩</a></li>
<li id="fn:213">MughalistanSipahi (19 June 2010). "Islamic Mughal Empire: War Elephants Part 3". Archived from the original on 13 December 2021. Retrieved 28 November 2012 – via YouTube. <a href="https://www.youtube.com/watch?v=Lbzr26t8H2U" target="_blank">https://www.youtube.com/watch?v=Lbzr26t8H2U</a> <a href="#fnref:213" class="footnote-back-ref">↩</a></li>
<li id="fn:214">Roddam Narasimha (1985), Rockets in Mysore and Britain, 1750–1850 A.D. Archived 27 September 2007 at the Wayback Machine, National Aeronautical Laboratory and Indian Institute of Science"Hyder Ali, prince of Mysore, developed war rockets with an important change: the use of metal cylinders to contain the combustion powder. Although the hammered soft iron he used was crude, the bursting strength of the container of black powder was much higher than the earlier paper construction. Thus a greater internal pressure was possible, with a resultant greater thrust of the propulsive jet. The rocket body was lashed with leather thongs to a long bamboo stick. Range was perhaps up to three-quarters of a mile (more than a kilometre). Although individually these rockets were not accurate, dispersion error became less important when large numbers were fired rapidly in mass attacks. They were particularly effective against cavalry and were hurled into the air, after lighting, or skimmed along the hard dry ground. Hyder Ali's son, Tippu Sultan, continued to develop and expand the use of rocket weapons, reportedly increasing the number of rocket troops from 1,200 to a corps of 5,000. In battles at Seringapatam in 1792 and 1799 these rockets were used with considerable effect against the British." – Encyclopædia Britannica (2008). rocket and missile. <a href="http://nal-ir.nal.res.in/2382/01/tr_pd_du_8503_R66305.pdf" target="_blank">http://nal-ir.nal.res.in/2382/01/tr_pd_du_8503_R66305.pdf</a> <a href="#fnref:214" class="footnote-back-ref">↩</a></li>
<li id="fn:215">A. Bowdoin Van Riper (29 October 2007). Rockets and Missiles: The Life Story of a Technology. JHU Press. pp. 14–. ISBN 978-0-8018-8792-5. <a href="978-0-8018-8792-5" target="_blank">978-0-8018-8792-5</a> <a href="#fnref:215" class="footnote-back-ref">↩</a></li>
<li id="fn:216">Narasimha, Roddam (27 July 2011). Rockets in Mysore and Britain, 1750–1850 A.D. (Report). National Aeronautical Laboratory and Indian Institute of Science. <a href="https://www.researchgate.net/publication/37179995" target="_blank">https://www.researchgate.net/publication/37179995</a> <a href="#fnref:216" class="footnote-back-ref">↩</a></li>
<li id="fn:217">Beckwith, Christopher I. (9 June 2015). Greek Buddha: Pyrrho's Encounter with Early Buddhism in Central Asia. Princeton University Press. ISBN 978-1-4008-6632-8. <a href="978-1-4008-6632-8" target="_blank">978-1-4008-6632-8</a> <a href="#fnref:217" class="footnote-back-ref">↩</a></li>
<li id="fn:218">Stephen Batchelor "Greek Buddha: Pyrrho's encounter with early Buddhism in central Asia", Contemporary Buddhism, 2016, pp 195–215 <a href="/wiki/Stephen_Batchelor_(author)" target="_blank">/wiki/Stephen_Batchelor_(author)</a> <a href="#fnref:218" class="footnote-back-ref">↩</a></li>
<li id="fn:219">Charles Goodman, "Neither Scythian nor Greek: A Response to Beckwith's Greek Buddha and Kuzminski's "Early Buddhism Reconsidered"", Philosophy East and West, University of Hawai'i Press Volume 68, Number 3, July 2018 pp. 984–1006 <a href="#fnref:219" class="footnote-back-ref">↩</a></li>
<li id="fn:220">Ganeri, Jonardon & Tiwari, Heeraman (eds.), (1988). The Character of Logic in India. Albany, NY, USA: State University of New York Press. ISBN 0-7914-3739-6 (HC:acid free), p.7-8 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:220" class="footnote-back-ref">↩</a></li>
<li id="fn:221">Ganeri, Jonardon (December 2002). "Jaina Logic and the Philosophical Basis of Pluralism". History and Philosophy of Logic. 23 (4): 267–281. doi:10.1080/0144534021000051505. <a href="https://philarchive.org/rec/JONJLA" target="_blank">https://philarchive.org/rec/JONJLA</a> <a href="#fnref:221" class="footnote-back-ref">↩</a></li>
<li id="fn:222">September 2017, Jessie Szalay-Live Science Contributor 18 (18 September 2017). "Who Invented Zero?". livescience.com. Retrieved 18 May 2021. {{cite web}}: |first= has generic name (help)CS1 maint: numeric names: authors list (link) <a href="https://www.livescience.com/27853-who-invented-zero.html" target="_blank">https://www.livescience.com/27853-who-invented-zero.html</a> <a href="#fnref:222" class="footnote-back-ref">↩</a></li>
<li id="fn:223">Nils-Bertil Wallin (19 November 2002). "The History of Zero". Yale Center for the Study of Globalization. Archived from the original on 25 August 2016. Retrieved 26 December 2011. <a href="https://web.archive.org/web/20160825124525/http://yaleglobal.yale.edu/about/zero.jsp" target="_blank">https://web.archive.org/web/20160825124525/http://yaleglobal.yale.edu/about/zero.jsp</a> <a href="#fnref:223" class="footnote-back-ref">↩</a></li>
<li id="fn:224">Dr. Hossein Arsham. "Zero in Four Dimensions". University of Baltimore. Retrieved 26 December 2011. <a href="http://home.ubalt.edu/ntsbarsh/zero/zero.htm" target="_blank">http://home.ubalt.edu/ntsbarsh/zero/zero.htm</a> <a href="#fnref:224" class="footnote-back-ref">↩</a></li>
<li id="fn:225">Devlin, Hannah (13 September 2017). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. <a href="https://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol" target="_blank">https://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol</a> <a href="#fnref:225" class="footnote-back-ref">↩</a></li>
<li id="fn:226">"Indian numerals". www-history.mcs.st-and.ac.uk. Retrieved 13 April 2015. <a href="http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_numerals.html" target="_blank">http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_numerals.html</a> <a href="#fnref:226" class="footnote-back-ref">↩</a></li>
<li id="fn:227">Salomon, R. (1998). Indian Epigraphy: A Guide to the Study of Inscriptions in Sanskrit, Prakrit, and the Other Indo-Aryan Languages. Oxford University Press, USA. p. 61. ISBN 9780195099843. Retrieved 13 April 2015. <a href="9780195099843" target="_blank">9780195099843</a> <a href="#fnref:227" class="footnote-back-ref">↩</a></li>
<li id="fn:228">Smith (1958), pp. 257–258 <a href="#fnref:228" class="footnote-back-ref">↩</a></li>
<li id="fn:229">Smith (1958), pp. 257–258 <a href="#fnref:229" class="footnote-back-ref">↩</a></li>
<li id="fn:230">Smith (1958), pp. 257–258 <a href="#fnref:230" class="footnote-back-ref">↩</a></li>
<li id="fn:231">Bourbaki (1998), page 49 <a href="#fnref:231" class="footnote-back-ref">↩</a></li>
<li id="fn:232">Britannica Concise Encyclopedia (2007). algebra <a href="#fnref:232" class="footnote-back-ref">↩</a></li>
<li id="fn:233">Bourbaki (1998), page 49 <a href="#fnref:233" class="footnote-back-ref">↩</a></li>
<li id="fn:234">Bell (1992), page 96 <a href="#fnref:234" class="footnote-back-ref">↩</a></li>
<li id="fn:235">Bell (1992), page 96 <a href="#fnref:235" class="footnote-back-ref">↩</a></li>
<li id="fn:236">Bell (1992), page 96 <a href="#fnref:236" class="footnote-back-ref">↩</a></li>
<li id="fn:237">Bell (1992), page 96 <a href="#fnref:237" class="footnote-back-ref">↩</a></li>
<li id="fn:238">Bell (1992), page 96 <a href="#fnref:238" class="footnote-back-ref">↩</a></li>
<li id="fn:239">Bell (1992), page 96 <a href="#fnref:239" class="footnote-back-ref">↩</a></li>
<li id="fn:240">Bell (1992), page 96 <a href="#fnref:240" class="footnote-back-ref">↩</a></li>
<li id="fn:241">Bell (1992), page 97 <a href="#fnref:241" class="footnote-back-ref">↩</a></li>
<li id="fn:242">"Al-Kindi biography". www-gap.dcs.st-and.ac.uk. Archived from the original on 26 October 2007. <a href="https://web.archive.org/web/20071026091801/http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Al-Kindi.html" target="_blank">https://web.archive.org/web/20071026091801/http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Al-Kindi.html</a> <a href="#fnref:242" class="footnote-back-ref">↩</a></li>
<li id="fn:243">"Bhaskaracharya II". Students' Encyclopedia India (2000). (Volume 1: Adb Allah ibn al Abbas – Cypress). p. 200. ISBN 0-85229-760-2 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:243" class="footnote-back-ref">↩</a></li>
<li id="fn:244">Kumar (2004), page 23 <a href="#fnref:244" class="footnote-back-ref">↩</a></li>
<li id="fn:245">Singh, Manpal (2005), page 385 <a href="#fnref:245" class="footnote-back-ref">↩</a></li>
<li id="fn:246">Plofker (2007), page 474 <a href="#fnref:246" class="footnote-back-ref">↩</a></li>
<li id="fn:247">Goonatilake (1998), page 127 – 128 <a href="#fnref:247" class="footnote-back-ref">↩</a></li>
<li id="fn:248">Goonatilake (1998), page 127 – 128 <a href="#fnref:248" class="footnote-back-ref">↩</a></li>
<li id="fn:249">Baber (1996), page 34 <a href="#fnref:249" class="footnote-back-ref">↩</a></li>
<li id="fn:250">"Bhaskaracharya II". Students' Encyclopedia India (2000). (Volume 1: Adb Allah ibn al Abbas – Cypress). p. 200. ISBN 0-85229-760-2 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:250" class="footnote-back-ref">↩</a></li>
<li id="fn:251">Goonatilake (1998), page 127 – 128 <a href="#fnref:251" class="footnote-back-ref">↩</a></li>
<li id="fn:252">Rao K. A. (2000), page 252 <a href="#fnref:252" class="footnote-back-ref">↩</a></li>
<li id="fn:253">Pingree (2003): "Geometry, and its branch trigonometry, was the mathematics Indian astronomers used most frequently. In fact, the Indian astronomers in the third or fourth century, using a pre-Ptolemaic Greek table of chords, produced tables of sines and versines, from which it was trivial to derive cosines. This new system of trigonometry, produced in India, was transmitted to the Arabs in the late eighth century and by them, in an expanded form, to the Latin West and the Byzantine East in the twelfth century." <a href="#fnref:253" class="footnote-back-ref">↩</a></li>
<li id="fn:254">J. J. O'Connor and E.F. Robertson (1996). Trigonometric functions Archived 20 January 2013 at the Wayback Machine. MacTutor History of Mathematics Archive <a href="http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Trigonometric_functions.html" target="_blank">http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Trigonometric_functions.html</a> <a href="#fnref:254" class="footnote-back-ref">↩</a></li>
<li id="fn:255">"Varahamihira biography". www-history.mcs.st-andrews.ac.uk. Retrieved 13 April 2015. <a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Varahamihira.html" target="_blank">http://www-history.mcs.st-andrews.ac.uk/Biographies/Varahamihira.html</a> <a href="#fnref:255" class="footnote-back-ref">↩</a></li>
<li id="fn:256">J. J. O'Connor and E. F. Robertson (2000). Paramesvara, MacTutor History of Mathematics archive. <a href="https://mathshistory.st-andrews.ac.uk/Biographies/Paramesvara/" target="_blank">https://mathshistory.st-andrews.ac.uk/Biographies/Paramesvara/</a> <a href="#fnref:256" class="footnote-back-ref">↩</a></li>
<li id="fn:257">Goonatilake (1998), page 37 <a href="#fnref:257" class="footnote-back-ref">↩</a></li>
<li id="fn:258">Amma (1999), pp. 182–183 <a href="#fnref:258" class="footnote-back-ref">↩</a></li>
<li id="fn:259">Goonatilake (1998), page 37 <a href="#fnref:259" class="footnote-back-ref">↩</a></li>
<li id="fn:260">Roy (1990) <a href="#fnref:260" class="footnote-back-ref">↩</a></li>
<li id="fn:261">Roy (1990) <a href="#fnref:261" class="footnote-back-ref">↩</a></li>
<li id="fn:262">Borwein (2004), page 107 <a href="#fnref:262" class="footnote-back-ref">↩</a></li>
<li id="fn:263">Plofker (2007), page 481 <a href="#fnref:263" class="footnote-back-ref">↩</a></li>
<li id="fn:264">Bressoud (2002) <a href="#fnref:264" class="footnote-back-ref">↩</a></li>
<li id="fn:265">Plofker (2001) <a href="#fnref:265" class="footnote-back-ref">↩</a></li>
<li id="fn:266">Katz (1995) <a href="#fnref:266" class="footnote-back-ref">↩</a></li>
<li id="fn:267">Stillwell 2004, p. 173. - Stillwell, John (2004). Mathematics and its History (2 ed.). Berlin and New York: Springer, 568 pages. ISBN 0-387-95336-1. <a href="#fnref:267" class="footnote-back-ref">↩</a></li>
<li id="fn:268">Van Brummelen, Glen (2009). The mathematics of the heavens and the earth: the early history of trigonometry. Princeton University Press. p. 329. ISBN 9780691129730. (p.111) <a href="9780691129730" target="_blank">9780691129730</a> <a href="#fnref:268" class="footnote-back-ref">↩</a></li>
<li id="fn:269">Meijering, Erik (March 2002). "A Chronology of Interpolation From Ancient Astronomy to Modern Signal and Image Processing". Proceedings of the IEEE. 90 (3): 319–342. doi:10.1109/5.993400. <a href="http://infoscience.epfl.ch/record/63085" target="_blank">http://infoscience.epfl.ch/record/63085</a> <a href="#fnref:269" class="footnote-back-ref">↩</a></li>
<li id="fn:270">Gupta, R. C. "Second-order interpolation in Indian mathematics upto the fifteenth century". Indian Journal of History of Science. 4 (1 & 2): 86–98. Reprinted as: Ramasubramanian, K. (2019). "Second-Order Interpolation in Indian Mathematics up to the Fifteenth Century". Gaṇitānanda. pp. 263–276. doi:10.1007/978-981-13-1229-8_27. ISBN 978-981-13-1228-1. <a href="978-981-13-1228-1" target="_blank">978-981-13-1228-1</a> <a href="#fnref:270" class="footnote-back-ref">↩</a></li>
<li id="fn:271">Bell (1992), page 96 <a href="#fnref:271" class="footnote-back-ref">↩</a></li>
<li id="fn:272">Bell (1992), page 96 <a href="#fnref:272" class="footnote-back-ref">↩</a></li>
<li id="fn:273">Bell (1992), page 96 <a href="#fnref:273" class="footnote-back-ref">↩</a></li>
<li id="fn:274">Knuth 2005, pp. 1–26. - Knuth, Donald (2005). Generating All Tuples and Permutations. The Art of Computer Programming. Vol. 4. Addison–Wesley. ISBN 978-0-201-85393-3. <a href="#fnref:274" class="footnote-back-ref">↩</a></li>
<li id="fn:275">Plofker (2007), pp. 419–436 <a href="#fnref:275" class="footnote-back-ref">↩</a></li>
<li id="fn:276">Joseph (2000), page 306 <a href="#fnref:276" class="footnote-back-ref">↩</a></li>
<li id="fn:277">Kala Fischbein, Tammy Brooks. "Brahmagupta's Formula". University of Georgia. Retrieved 3 November 2011. <a href="http://jwilson.coe.uga.edu/EMT725/Class/Brooks/Brahmagupta/Brahmagupta.html" target="_blank">http://jwilson.coe.uga.edu/EMT725/Class/Brooks/Brahmagupta/Brahmagupta.html</a> <a href="#fnref:277" class="footnote-back-ref">↩</a></li>
<li id="fn:278">Weisstein, Eric W. "Brahmagupta Matrix". Mathworld. Retrieved 3 November 2011. <a href="http://mathworld.wolfram.com/BrahmaguptaMatrix.html" target="_blank">http://mathworld.wolfram.com/BrahmaguptaMatrix.html</a> <a href="#fnref:278" class="footnote-back-ref">↩</a></li>
<li id="fn:279">"India". Archived from the original on 14 November 2007. Retrieved 5 March 2008. <a href="https://web.archive.org/web/20071114201718/http://binomial.csueastbay.edu/India.html" target="_blank">https://web.archive.org/web/20071114201718/http://binomial.csueastbay.edu/India.html</a> <a href="#fnref:279" class="footnote-back-ref">↩</a></li>
<li id="fn:280">Hall, Rachel (16 February 2005). "Math for Poets and Drummers-The Mathematics of Meter" (PDF). Archived from the original (PDF) on 7 September 2008. Retrieved 5 March 2008. {{cite journal}}: Cite journal requires |journal= (help) <a href="https://web.archive.org/web/20080907145421/http://www.sju.edu/%7Erhall/Rhythms/poets.pdf" target="_blank">https://web.archive.org/web/20080907145421/http://www.sju.edu/%7Erhall/Rhythms/poets.pdf</a> <a href="#fnref:280" class="footnote-back-ref">↩</a></li>
<li id="fn:281">Kulkarni, Amba (2007). Recursion and Combinatorial Mathematics in Chandashaastra (Preprint). arXiv:math/0703658. Bibcode:2007math......3658K. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:281" class="footnote-back-ref">↩</a></li>
<li id="fn:282">Datta, Bibhutibhusan; Singh, Awadhesh Narayan (2019). "Use of permutations and combinations in India". In Kolachana, Aditya; Mahesh, K.; Ramasubramanian, K. (eds.). Studies in Indian Mathematics and Astronomy: Selected Articles of Kripa Shankar Shukla. Sources and Studies in the History of Mathematics and Physical Sciences. Springer Singapore. pp. 356–376. doi:10.1007/978-981-13-7326-8_18. ISBN 978-981-13-7325-1. S2CID 191141516.. Revised by K. S. Shukla from a paper in Indian Journal of History of Science 27 (3): 231–249, 1992, MR1189487. See p. 363. <a href="978-981-13-7325-1" target="_blank">978-981-13-7325-1</a> <a href="#fnref:282" class="footnote-back-ref">↩</a></li>
<li id="fn:283">Goonatilake, S. (1998). Toward a Global Science: Mining Civilizational Knowledge. Indiana University Press. p. 126. ISBN 9780253333889. Retrieved 13 April 2015. <a href="9780253333889" target="_blank">9780253333889</a> <a href="#fnref:283" class="footnote-back-ref">↩</a></li>
<li id="fn:284">"Varahamihira biography". www-history.mcs.st-andrews.ac.uk. Retrieved 13 April 2015. <a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Varahamihira.html" target="_blank">http://www-history.mcs.st-andrews.ac.uk/Biographies/Varahamihira.html</a> <a href="#fnref:284" class="footnote-back-ref">↩</a></li>
<li id="fn:285">Edwards, A.W.F. (2002). Pascal's Arithmetical Triangle: The Story of a Mathematical Idea. Johns Hopkins University Press. p. 201. ISBN 9780801869464. Retrieved 13 April 2015. <a href="9780801869464" target="_blank">9780801869464</a> <a href="#fnref:285" class="footnote-back-ref">↩</a></li>
<li id="fn:286">Puttaswamy (2000), page 416 <a href="#fnref:286" class="footnote-back-ref">↩</a></li>
<li id="fn:287">Stillwell 2004, pp. 72–73. - Stillwell, John (2004). Mathematics and its History (2 ed.). Berlin and New York: Springer, 568 pages. ISBN 0-387-95336-1. <a href="#fnref:287" class="footnote-back-ref">↩</a></li>
<li id="fn:288">Stillwell (2004), pages 72–73 <a href="#fnref:288" class="footnote-back-ref">↩</a></li>
<li id="fn:289">Joseph, G. G. (2011), The Crest of the Peacock: Non-European Roots of Mathematics (3rd ed.), Princeton University Press, p. 352. <a href="/wiki/The_Crest_of_the_Peacock:_Non-European_Roots_of_Mathematics" target="_blank">/wiki/The_Crest_of_the_Peacock:_Non-European_Roots_of_Mathematics</a> <a href="#fnref:289" class="footnote-back-ref">↩</a></li>
<li id="fn:290">See, e.g., Shparlinski, Igor (2013), Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness, Progress in Computer Science and Applied Logic, vol. 22, Birkhäuser, p. 35, ISBN 978-3-0348-8037-4. <a href="978-3-0348-8037-4" target="_blank">978-3-0348-8037-4</a> <a href="#fnref:290" class="footnote-back-ref">↩</a></li>
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</ol>

List of Indian inventions and discoveries open-in-new

List of Indian inventions and discoveries