mildred_of_midgard: (Default)
mildred_of_midgard ([personal profile] mildred_of_midgard) wrote in [personal profile] cahn 2022-06-11 02:18 pm (UTC)

Yeah, the whole point of geometry is that proto-geometry started off as people making observations about the real world, and going, "This is probably a valid generalization!" and then the breakthroughs came when people started doing *deductive* logic and proving that, for example, the square of the hypotenuse will *always* (given axioms of Euclidean geometry) be equal to the sum of the squares of the sides. Always always, not just "For the 49 triangles I checked before I got bored, and I don't know if the 50th would have been a counterexample."

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