I learned an interesting Pythagoras proof today. Note that the yellow subtriangles are congruent tot the main yellow triangle.pic.twitter.com/HnQTje1RDt
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The hypotenuse of the main yellow triangle is c, so the two yellow subtriangles result from scaling it down by a/c and b/c. The main yellow triangle's hypotenuse is divided into pieces of lengths (a^2)/c and (b^2)/c, so the rectangles on these segments have areas a^2 and b^2.
Thanks. I suppose the (a^2)/c comes from a.(a/c) and (b^2)/c from b.(b/c).
Yes, that's right.
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