A few days ago Sarah was asking if any of us had had a Little Professor and when I clicked through to see what she was talking about I realized I'd had one. I have a positive associations with the Little Professor, although other recognizing that I'd had one I don't remember anything else (like playing calculator games). Just a few minutes ago, for no reason in particular except it is 50 minutes until State Employee Appreciation Proclamation reading and snacks, I was thinking about the geekiest thing I did as a kid.
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 ex 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:
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.