Okay, this is going to be a pretty feeble attempt to get the ball rolling. Tomorrow I will mention that we use deductive reasoning when we apply Pythagoras' theorem to solve for a length in a specific right triangle. For example, if we know that a right triangle has sides with length 12 and 5, then the hypotenuse must have length = 13 because 12^2 + 5^2 = 13^2. The real reason I want to mention this is because of something cool I learned earlier this year. The Flatiron Building in New York City is a right triangle, and its sides are in the proportions 12-5-13. The Museum of Mathematics in NYC held an event on Dec 5, 2013 (12-5-13) to demonstrate this. They even used glow-sticks! Here are two links about it:
Pythagorazing the Flatiron
Glow Sticks Prove Math Theorem
I went to New York this summer and of course had to go to the Museum of Math MoMath, it was awesome. It is just off Broadway, and I could see the Flatiron Building as I walked to the museum from the subway station. Considering how large New York is, that is pretty cool. One of my research areas is fractal trees, and the museum had a fun activity that turned me into a fractal tree.
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