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Q&A #7222


Teaching e

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Nov 05, 2001 at 13:49:15
Subject: Re: Teaching e

Dear Rae,

The base of the natural logs, e, is a topic well beyond any single answer I
could give you, but for starters, here are some things that might help...
A VERY brief intro at my web page
http://www.geocities.com/poetsoutback/etyindex.html
  look under "e" of course...

also at the math forum Dr. Math FAQ page
http://mathforum.org/dr.math/faq/faq.e.html

A couple of brief reasons why e is important and related to calculus...

The slope of the curve a^x depends, of course on a, but when a = e, then the
slope at any point is equal to the y-value, that is, the slope of e^x is
equal to e^x...

At the discovery of logarithms, people quickly realized that the area under
y=1/x from x=1 to some value x=c is related to the idea of logarithms...
interestingly , the area under the curve is exactly one when the area is
taken from x=1 to x=e....

and of course, it is one of the five basic numbers of math that show up in
what many mathematicians call the most beautiful theorem of all time,
Euler's famous e^(pi * i) + 1 = 0..

Hope some of that helps..

 -Pat Ballew, for the T2T service

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