**Constant Growth**

Certain numbers show up over and over again in mathematical descriptions of the natural world. These numbers are known as "constants." We'll talk with a mathematician about the constant known as "e" - after this on Earth and Sky.

**Date
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DB: This is Earth and Sky, on a special kind of number -- known as a "mathematical constant" -- that's very useful in describing certain patterns in nature. It's a number known simply as "e" -- and it's roughly 2.72. We spoke with Dr. David Harbater, a mathematician at the University of Pennsylvania, about the number e:

(Tape 0:17:39-0:17:58) Let's suppose you had a dollar, just to take a round amount, and you put it into a bank account. And to simplify things, imagine you had a hundred percent interest every year -- more than you'd really get, but just to simplify things. Now, if you had simple interest, at the end of the year you'd get a dollar interest on top of your dollar -- you'd have two dollars. (Tape 0:18:11-0:18:16) Suppose the bank compounded it every month, or every day, or every hour, or every second, or every instant.

(Tape 0:18:23-0:18:28) Would you end with three dollars, five dollars, a million dollars, a billion dollars? What would happen? (Tape 0:18:36-0:18:54) The amount you end up with is just under two dollars and seventy-two cents. And in fact that quantity is actually the number e, which winds up coming up in a lot of situations in mathematics and in the real world having to do with growth.

DB: The number e shows up not only in the growth of money, but in the growth patterns of snail shells, spiral galaxies, and even the spread of information. Thanks to Dr. David Harbater for speaking with us. And with thanks to the National Science Foundation, I'm Deborah Byrd, for Joel Block, for Earth and Sky.

Author: Beverly Wachtel

Thanks to the following individual for aiding in the preparation of this script:

Dr. David Harbater

Department of Mathematics

University of Pennsylvania

Philadelphia, PA

Harbater@math.upenn.edu

If you enjoyed this program, you may be interested in the following:

*e: The Story of A Number*, Eli Maor. Princeton: Princeton University Press, 1993.

Mathematical Constants and Interesting Numbers:

http://www.abc.se/~m9847/constans.html

Favorite Mathematical Constants:

http://pauillac.inria.fr/algo/bsolve/constant/constant.html

Mathematical Sciences Research Institute:

http://www.msri.org