# How was the number 'e' 2.718 originated?

1. Aug 28, 2011

### PrakashPhy

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.... .

<<<sorry if this thread already exists in the forum; i searched in the forum but couldn't find it>>>

2. Aug 28, 2011

### wukunlin

http://en.wikipedia.org/wiki/Euler's_number#History

3. Aug 28, 2011

### PrakashPhy

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

4. Aug 28, 2011

### gb7nash

And with a little more digging...

http://en.wikipedia.org/wiki/Jacob_Bernoulli

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.

5. Aug 28, 2011

### Dr. Seafood

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
6. Aug 28, 2011

### JDoolin

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

\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*}

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

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