the number "e"

MathIsGreat · P versus NP Offline Joined: 20 Jan 2008 Posts: 32

How did the number e come about?
Please explain.
Thanks.

**Posted:** Thu Nov 05, 2009 9:27 pm

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mavropnevma

There is no point in copy-and-paste well-written materials. A search on Google using keywords "Euler's number" gives a lot of links, first being http://en.wikipedia.org/wiki/E_(mathematical_constant)

**Posted:** Thu Nov 05, 2009 10:51 pm

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1=2

Note: this story will make sense if you know the definition of the derivative.
Someone decided to take the derivative of the function $f(x)=c^x$ where $c$ is a constant, and got $c^x*\lim_{x\rightarrow 0}\frac{e^x-1}{x}$ . Note that $\lim_{x\rightarrow 0}\frac{c^x-1}{x}$ is a constant given $c$ . So someone decided to prove that there existed a constant $e$ such that $\lim_{x\rightarrow 0}\frac{e^x-1}{x}=1$ , which means $\frac{d}{dx}[e^x]=e^x$ . Then plugging in 1 into the Taylor Series of $f(x)=e^x$ (with $a=0$ [Wikipedia the Taylor Series]), you get $\frac{1}{1}+\frac{1}{1!}+\frac{1}{2!}+\cdots$ , which equals $e$ .

**Posted:** Fri Nov 06, 2009 4:27 am

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Hmm... apparently quoting Disney movies gets me muted on FTW. Razz

mathkid95

It's from Euler. It is used for interest problems that compound continuously.

ex.

ln 7.4 = 2

It is log natural

**Posted:** Sat Nov 07, 2009 8:08 am

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Rotfl

$\text{M^{A}T H_{R^{U_{L_{E{S}}}}}}$

Dr Sonnhard Graubner

hello, see also here
http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Exponential_Function.pdf
Sonnhard.

**Posted:** Sat Nov 07, 2009 8:14 am