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How is this story obviously wrong if you've developed the Pythagorean theorem? The Pythagorean theorem has nothing to do with rationality. If you think the ir
by Sniffnoy 2y ago
How is this story obviously wrong if you've developed the Pythagorean theorem? The Pythagorean theorem has nothing to do with rationality. If you think the irrationality of sqrt(2) follows easily from the Pythagorean theorem, then by all means, please demonstrate!
(These days the irrationality of sqrt(2) is obvious due to unique prime factorization, but the ancient Greeks didn't have that concept!)
- dr_dshiv 2y agoIt’s because you can’t create square root of two with a fraction. Pythagoreans were all about fractions (such as their musical tuning).
- Sniffnoy 2y agoThat's not an argument, that's a restatement of the problem; that's what being irrational means. The problem is to prove that you can't create sqrt(2) with a fraction. How, exactly, would this statement have been obvious to the Pythagoreans? Can you give me an argument for this that they would have found obvious? One that uses the Pythagorean theorem even, perhaps, since you brought that up? Remember, no using concepts they wouldn't have had like prime factorization!