I’m embarrassed to admit this, but I had never realized that the Pythagorean Theorem’s a^2 + b^2 = c^2 actually meant “the area of the square made by the side length C is the same as the sum of the areas made by the squares made of the other two sides’ side lengths” until I was in graduate school. When I saw it for the first time in Professor Oliver Knill’s class, aside from his animation being totally bad ass, I was totally blown away by the realization of what I had never realized.
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So here are some animations, starting with Oliver’s, that show how awesomely dynamic Pythagoras’s theorem is:
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