Phil 160D2
Mind, Matter and God

Pythagorean Theorem

Consider a square X whose sides c equal the hypotenuse of right triangle abc. Embed X in a larger square Y whose sides = a+b such that the corners of X each meet a side of Y. Then:

(a+b)x(a+b) = c2 + 4((axb)/2)

(a+b)x(a+b) - 4((axb)/2) = c2

a2+ab+b2+ab - 2(ab) = c2

a2+b2 = c2

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