Similarly, Pythagoras' theorem turns out not to be literally about "squares" but about squaring as what happens to area under linear scaling. Mathematicians see

Similarly, Pythagoras' theorem turns out not to be literally about "squares" but about squaring as what happens to area under linear scaling. Mathematicians seem to find this proof more satisfying than most of the many proofs available, as it points towards the reason for the identity... Something to do with right angles in Euclidean space. I'm afraid this is not a prestigious source but my Google-fu is failing me. Polyps mentions this proof, as has Terry Tao more recently: https://betterexplained.com/articles/surprising-uses-of-the-pythagorean-theorem/ https://betterexplained.com/articles/surprising-uses-of-the-... Edit: more credible discussion here: https://math.berkeley.edu/~giventh/papers/eu.pdf https://math.berkeley.edu/~giventh/papers/eu.pdf