Tattoos in a square

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Let a, b and c be the sides of the right triangle. The area of the middle square is clearly c^2. However, that is also the large square ((a+b)^2), removing the four triangles (ab/2 each). Subtracting, you get a^2+b^2.    For the inequality, the big square ((a+b)^2) is larger than the four rectangles (ab each), as the tiny square has area. Taking the square root and dividing gives (a+b)/2 > sqrt{ab}. (Note that when a=b, the square in the middle goes to 0, and we have equality. Patchwork, Geometric Simple Tattoo, Pythagoras Tattoo, Math Tattoo, Geeky Tattoos, Remember Tattoo, Square Tattoo, Clover Tattoos, Pythagorean Theorem

It’s a simple tattoo, but oh so important in the world of math. And it’s on a super geek. (He even sent a latexed version of the proof). For those that aren’t familiar, it’s a pictorial proof of the Pythagorean Theorem / Means Inequality. Here’s Sam’s explanation: Let a, b and c be the sides […]