For as long as I can remember I've taken long showers. When I'm not falling asleep in them, my mind is wandering; sometimes I'm doing both. I used to, sometimes, do math in the shower. (BTW, I find steamed up tiles are excellent righting surfaces, far superior to my current plastic tub surround.) About the same time I was playing with my brother's scientific calculator to try and figure out what e

^{x}and ln(x) meant. (And sneak some of that advanced intermediate school knowledge denied my elementary school self.) I also was trying to figure out X². My brother explained exponents to me and I knew my times tables up to 12*12, so I thought this was pretty cool.

So one morning in the shower I figured out 13² and 14² and 15² and then I wondered if there was an easy way to figure out a square without having to do all that multiplication. I proceeded to re-invented algebra. The way to do this algebraically isn't any simpler but it did allow me to figure out the square of 13 (and 14, 15, ...) without doing any multiplication by hand.

Here's what I figured out:

12²+12+13=13²=163

Little did I know that I'd just figured out that

(X+1)² = X² + 2x +1

I immediately recognized this later when I took algebra. There it is, I was a hopeless geek at 9.

## No comments:

Post a Comment