Thursday, October 20, 2005

Andrew Jackson and the number e

·

I just read this over at the brightMystery blog. A cool way to learn about e; especially if you're American. ;-)


brightMystery
He who wonders discovers that this in itself is wonder. -- M. C. Escher

Andrew Jackson and the number e

By robert on math

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:
aj.jpg

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:
aj-diag.jpg

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.]

5 comments:

Downes said...
21/10/05 15:47  

Hey, what a great way for me to remember that Andrew Jackson was the 7th president and elected in 1898!

Downes said...
21/10/05 16:06  

um... 1828...

Anonymous said...
26/9/07 21:58  

I think he was president twice; hence 1828 1828

KEE TEO, New Zealand

Joey Travelli said...
13/11/08 18:45  

Sweet, I heard this at BSU in 2000! Ah, memories... and yes, 1829-1837, two terms...

Anonymous said...
7/1/13 11:22  

I was taught this in my calculus class at the University of Rochester in the fall of 1968.

Learning about learning ...

While walking ...
Best viewed "full screen." (Click on bottom right corner of any video when playing.)

With pictures ...
Best viewed "full screen." (Click on bottom right corner of any image when playing.)

Curating discoveries ...


Archives

Creative Commons License
This work is licensed under a Creative Commons Licence.

My Class Blogs

Class Blog 2004-2005
Class Blogs 2005 - 2006
Class Blogs 2006 - 2007
Class Blogs 2007 - 2008
Class Blogs 2008 - 2009

Delicious Links