Al-Khwarizmi

Muhammad ibn Musa al-Khwarizmi , or simply al-Khwarizmi, was a prominent <a href="/facts/Mathematician/eaFSR8Fx">mathematician</a> from the <a href="/facts/Islamic_Golden_Age/yAeG2rBA">Islamic Golden Age</a>, who produced Arabic-language works in <a href="/facts/Mathematics_in_the_medieval_Islamic_world/TACUEnlp">mathematics</a>, <a href="/facts/Astronomy_in_the_medieval_Islamic_world/hw8HxDHz">astronomy</a>, and <a href="/facts/Geography_and_cartography_in_the_medieval_Islamic_world/RFokhUH6">geography</a>. Around 820, he worked at the <a href="/facts/House_of_Wisdom/Iyo9lg8a">House of Wisdom</a> in <a href="/facts/Baghdad/RbtLzzHe">Baghdad</a>, the contemporary capital city of the <a href="/facts/Abbasid_Caliphate/mPeLAbXt">Abbasid Caliphate</a>. His works were widely influential on later authors, both in the Islamic world and Europe.
His popularizing treatise on <a href="/facts/Algebra/nMdqczjo">algebra</a>, compiled between 813 and 833 as <a href="/facts/Al-Jabr/lxWsG6WD">Al-Jabr</a> (The Compendious Book on Calculation by Completion and Balancing),: 171  presented the first systematic solution of <a href="/facts/Linear_equation/JfCgALwf">linear</a> and <a href="/facts/Quadratic_equation/9IMnkJAT">quadratic equations</a>. One of his achievements in <a href="/facts/Algebra/nMdqczjo">algebra</a> was his demonstration of how to solve quadratic equations by <a href="/facts/Completing_the_square/SN6xA8sc">completing the square</a>, for which he provided geometric justifications.: 14  Because al-Khwarizmi was the first person to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The English term algebra comes from the short-hand title of his aforementioned treatise (الجبر Al-Jabr, transl. "completion" or "rejoining"). His name gave rise to the English terms <a href="/facts/Algorism/btA0FVxc">algorism</a> and <a href="/facts/Algorithm/fnl5NmRt">algorithm</a>; the Spanish, Italian, and Portuguese terms algoritmo; and the Spanish term guarismo and Portuguese term algarismo, both meaning '<a href="/facts/Numerical_digit/JJdLBoGT">digit</a>'.
In the 12th century, Latin translations of al-Khwarizmi's textbook on Indian arithmetic (Algorithmo de Numero Indorum), which codified the various <a href="/facts/Indian_numerals/z73KvotW">Indian numerals</a>, introduced the <a href="/facts/Decimal/7omfVNIM">decimal</a>-based <a href="/facts/Positional_notation/31DECoN4">positional number system</a> to the <a href="/facts/Western_world/UQl4e7du">Western world</a>. Likewise, Al-Jabr, translated into Latin by the English scholar <a href="/facts/Robert_of_Chester/jgf8rTdt">Robert of Chester</a> in 1145, was used until the 16th century as the principal mathematical textbook of <a href="/facts/List_of_medieval_universities/NmKpDraK">European universities</a>.
Al-Khwarizmi revised <a href="/facts/Geography_(Ptolemy)/gbCXgJR7">Geography</a>, the 2nd-century Greek-language treatise by <a href="/facts/Ptolemy/htudGQTQ">Ptolemy</a>, listing the longitudes and latitudes of cities and localities.: 9  He further produced a set of astronomical tables and wrote about calendric works, as well as the <a href="/facts/Astrolabe/BctVIEm4">astrolabe</a> and the <a href="/facts/Sundial/RWM823m2">sundial</a>. Al-Khwarizmi made important contributions to <a href="/facts/Trigonometry/K4hfaC6F">trigonometry</a>, producing accurate <a href="/facts/Sine_and_cosine/0UtQ97vu">sine and cosine</a> tables and the first table of <a href="/facts/Tangent/sF0jH3EI">tangents</a>.

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Al-Khwarizmi