Teacher2Teacher |
Q&A #7222 |
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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