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How was the number 'e' 2.718 originated?

  1. Aug 28, 2011 #1
    Since past two years I have been using the mathematical constant 'e' over and again in mathematics (calculus and logarithm). I wonder how this number first originated. Who first used this number , this particular number e=2.718281828459045.... .

    Thank you for your help in advance.

    <<<sorry if this thread already exists in the forum; i searched in the forum but couldn't find it>>>
  2. jcsd
  3. Aug 28, 2011 #2


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  4. Aug 28, 2011 #3
    How at once did he encounter this limit? There must have been some earlier equations or problems or something that led to this equation.

    Like pi =3.14... is the ratio of circumference of a circle to its diameter which is a simplest way to understand pi and probably which is the origin of of pi ; I wish to get such simpler and similar information on origin of e
  5. Aug 28, 2011 #4


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    And with a little more digging...


    That's how it was discovered anyway. As far as what uses it has, the more time that passed, the more people that found a particular use for e. ex is the only function who's derivative is equal to itself. e is a key component of Euler's identity. etc.
  6. Aug 28, 2011 #5
    Check http://summer-time-nerd.tumblr.com/post/8628678169" [Broken] out (it's my blog :)). Apparently Bernoulli (one of them :p) explored this finance problem, where he encountered this limit in this theoretical situation.
    Last edited by a moderator: May 5, 2017
  7. Aug 28, 2011 #6


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    Another useful definition of e can be found by taking the taylor series (more specifically, the Maclaurin series) of e^x.

    [tex]\begin{align*} e^{x} &= \sum_{n=0}^\infty \frac{( x)^n }{n !} \\ e^1 &= \frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!} +...\\ &=1+1 +\frac{1}{2}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}+... \end{align*}[/tex]

    If you do the same for sine and cosine, and e(i x)
    [tex] e^{ix} = \sum_n \frac{(i x)^n }{n !} [/tex]

    you'll find a very clear relationship between the exponential functions and the trigonometric functions, using complex numbers.
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