I'm just never satisfied by any "proofs" of the pythagorean theorem. Can someone give me insight why the sum of areas of similar shapes on two sides equals the area of another similar shape on the diagonal side? Seriously, why? It's just completely no intuition there.

Question

kainui · Answer

Those are exactly what _don't_ help.

kainui · Answer

Nothing about rearranging cut out squares is intuitive. I'm looking for a deeper answer. If for some reason the pythagorean theorem was a^3+b^3=c^3 and they drew it all out with volumes and it matched up I'd be equally as dissatisfied.

anonymous · Answer

to tell you the truth much math in that era was drawn and then solve theoretically so i dont think you can really get away from drawing squares to = hypot square

kainui · Answer

Yeah, I don't think either of you get where I'm coming from. I've seen many different things like this, but none of them make it intuitive. For instance, I like this:

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$$(a+b)^2=4*\frac{ 1 }{ 2 }ab+c^2$$
it follows, 

a^2+b^2=c^2

But that doesn't EXPLAIN anything, only SHOWS that it is true. WHY?

primeralph · Answer

@Kainui  Hold on.

primeralph · Answer

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