Me vs. Pythagoras. You know when you set out to prove something wrong, then end up proving your own preconceptions wrong instead? Yea, so I've been thinking about the pythagorean theorem for the last couple days. There's no real written record about how Pythagoras "discovered" it (though it had also been discovered by other civilizations like the Babylonians and the Chinese). Anyways, as one legend has it, Pythagoras was in a tiled courtyard and after staring at the tiles for awhile, he miraculously uncovered his famous a^2+b^2=c^2.
Well frankly, I didn't buy it. You see, I too have spent many hours of my life staring at tiles. When I'm in the bathroom, my mind just wanders, and I find myself staring at the floor tiles. In the honors dorms the past two years, I had a little project of uncovering all the possible configurations of tiles that would tesselate (; I came to the conclusion that any four adjacent tiles could be tesselated to form the floor design). This year, Jester's bathroom tiles are a lot less interesting- the only thing remotely interesting is the random color distribution. My potty-time mini-project this year consists mainly of developing pattern recognition techniques. Anyways, I digress...
So I was thinking about tesselations a lot and decided that you couldn't tesselate a design that would lead to the revelation of the pythagorean theorem. My logic was that the simplest pythagorean triples lead to angles that would be too hard to cut consistently for tiles. Perhaps this was my folly: to focus on integer values for the sides instead of angles. To my knowledge, the only right triangles that anyone would reasonably make into a tile pattern would be 30-60-90's and 45-45-90's. The former doesn't lead to any geometric squares. It wasn't until I got a good look at a pattern of 45-45-90's that I finally saw it- buried amidst the clutter, is that classic chubby Y-shaped figure used to teach kids the world over. Foolish me for ever doubting, haha. Pythagoras- 1, me- 0. Still though, could you extrapolate a theorem for all triangles based on just the standard right isosceles? But that was just me being obstinate again, cuz after a bit more thought, I realized that if you toss a square or two into the mix, there's actually several tesselations that would yield the pythagorean theorem. Dang, score one more for the Greek.
Game, set, match- Pythagoras.
Well frankly, I didn't buy it. You see, I too have spent many hours of my life staring at tiles. When I'm in the bathroom, my mind just wanders, and I find myself staring at the floor tiles. In the honors dorms the past two years, I had a little project of uncovering all the possible configurations of tiles that would tesselate (; I came to the conclusion that any four adjacent tiles could be tesselated to form the floor design). This year, Jester's bathroom tiles are a lot less interesting- the only thing remotely interesting is the random color distribution. My potty-time mini-project this year consists mainly of developing pattern recognition techniques. Anyways, I digress...
So I was thinking about tesselations a lot and decided that you couldn't tesselate a design that would lead to the revelation of the pythagorean theorem. My logic was that the simplest pythagorean triples lead to angles that would be too hard to cut consistently for tiles. Perhaps this was my folly: to focus on integer values for the sides instead of angles. To my knowledge, the only right triangles that anyone would reasonably make into a tile pattern would be 30-60-90's and 45-45-90's. The former doesn't lead to any geometric squares. It wasn't until I got a good look at a pattern of 45-45-90's that I finally saw it- buried amidst the clutter, is that classic chubby Y-shaped figure used to teach kids the world over. Foolish me for ever doubting, haha. Pythagoras- 1, me- 0. Still though, could you extrapolate a theorem for all triangles based on just the standard right isosceles? But that was just me being obstinate again, cuz after a bit more thought, I realized that if you toss a square or two into the mix, there's actually several tesselations that would yield the pythagorean theorem. Dang, score one more for the Greek.
Game, set, match- Pythagoras.
posted by Dear Daniel at 7:57 PM
1 Comments:
I noticed that awhile ago, myself. I didn't think that ANYONE could pick that up from staring at floor tiles. Until I found the Y-triangle patterns, and then it became blatently obvious to me. I felt like a sucker. I think all the easy theorems have been proven already. Gotta find another one...
-EddY
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