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Proof 1: Dimensional Analysis - by Anjor

pythproofs.substack.com · 276 words · saved by 1 readers

This is by far my favourite proof of the Pythagorean theorem.

This is by far my favourite proof of the Pythagorean theorem. It’s elegant, simple and appeals to the physicist in me. Take a right triangle. Call the hypotenuse c, and let θ be one of the two non-right angles. Those two numbers pin the triangle down completely — fix a hypotenuse and one angle and there's exactly one such right triangle. So its area is some function of just θ and c: \(\text{Area} = f(\theta, c)\) Area has units of length². The angle θ is dimensionless. The only length anywhere in the problem is c. So by dimensional analysis, the only form area can take is as follows:…

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