Andrew Jackson and the number e10/20/2005 11:13:00 pm
I just read this over at the brightMystery blog. A cool way to learn about e; especially if you're American. ;-)
He who wonders discovers that this in itself is wonder. -- M. C. Escher
I'm going into isolation for the next couple of days to work on my CV and tenure portfolio, all of which is due on November 11. But I thought I'd give you something extremely clever and cool to think about, which I learned over the weekend. This is due to my colleague Bill Murphy, who teaches precalculus for us here. (And he attributes it to his wife, who is a high school social studies teacher.)
In mathematics, the number e is a constant used a lot in calculus and related fields. It is an irrational number, which means it has an infinite, non-repeating decimal expansion. (Here's a proof.) A 15-place approximation to this number is
e = 2.718281828459045
Here's how to memorize that 15-place approximation. First of all, memorize by rote the fact that the ones digit for e is 2. To memorize the 15 decimal places, we invoke the following perfectly square picture of Andrew Jackson:
Andrew Jackson was our seventh president. And he was elected in 1828. Using these facts, you can memorize the "7" and the "1828" in the decimal expansion. And if you remember that this is a square photo, you can remember to label both the height and the width of the photo with "1828", so you get two copies of "1828" in the decimal expansion. So now we have a way of remembering e = 2.718281828.
For the remaining six digits, remember that this is a SQUARE picture. So draw a diagonal:
The diagonal splits the square into two triangles. Think back on basic geometry. What are the angle measures in one of those triangles? You guessed it: 45-90-45. And those are the remaining six digits of the decimal expansion: 2.718281828459045.
So now you can amaze/impress/alienate your friends by spouting off the value of e to 15 places at will. And you learn a little about one of our Presidents in the process. Cool geek stuff, no?
[Update: If you start with the picture first, you don't have to memorize the ones digit of 2 by rote. Just remember that if you "square" something it means raising it to the power of 2, and there you go.]