chrisheaven
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why?
Actually, the proof that √2 is irrational greatly upset the mathematical school of Pythangorus. One of the Pythagoreans is alleged to have committed suicide because of it. 😱
Since those same Greeks believed that any two physical lengths were commensurable*, that is what upset them greatly.Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational!
Since those same Greeks believed that any two physical lengths were commensurable*, that is what upset them greatly.
*both whole number multiples of a common smaller length
Correct. 😀yes-- they were of course mistaken in this belief