e (mathematical constant)

<p>The number e is a <a href="/facts/Mathematical_constant/rzqTX307">mathematical constant</a> approximately equal to 2.71828 that is the <a href="/facts/Base_of_a_logarithm/QeXaV97q">base</a> of the <a href="/facts/Natural_logarithm/PnreKEzI">natural logarithm</a> and <a href="/facts/Exponential_function/ewlYxvR2">exponential function</a>. It is sometimes called Euler's number, after the Swiss mathematician <a href="/facts/Leonhard_Euler/z2fsbjgj">Leonhard Euler</a>, though this can invite confusion with <a href="/facts/Euler_numbers/acpKy6uS">Euler numbers</a>, or with <a href="/facts/Euler%27s_constant/2kEgRvjC">Euler's constant</a>, a different constant typically denoted 
  
    
      
        γ
      
    
    {\displaystyle \gamma }
  
. Alternatively, e can be called Napier's constant after <a href="/facts/John_Napier/Wg0HAmq5">John Napier</a>. The Swiss mathematician <a href="/facts/Jacob_Bernoulli/rUnwozsy">Jacob Bernoulli</a> discovered the constant while studying compound interest.
</p><p>The number e is of great importance in mathematics, alongside 0, 1, <a href="/facts/Pi/vC0UBj1q">π</a>, and <a href="/facts/Imaginary_unit/1SCllQlU">i</a>. All five appear in one formulation of <a href="/facts/Euler%27s_identity/QB4HQun8">Euler's identity</a> 
  
    
      
        
          e
          
            i
            π
          
        
        +
        1
        =
        0
      
    
    {\displaystyle e^{i\pi }+1=0}
  
 and play important and recurring roles across mathematics. Like the constant π, e is <a href="/facts/Irrational_number/Psv19TET">irrational</a>, meaning that it cannot be represented as a ratio of integers, and moreover it is <a href="/facts/Transcendental_number/IrB7JppM">transcendental</a>, meaning that it is not a root of any non-zero <a href="/facts/Polynomial/Lzak8VVx">polynomial</a> with rational coefficients. To 30 decimal places, the value of e is:
</p>
2.718281828459045235360287471352

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e (mathematical constant)