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The square root of two, the length of the diagonal of a square with side length one. A clever proof shows that if the square root of two were actually the ratio of two integers, then we could produce an integer that is both even and odd. Impossible! Irrefutable proof that the Pythagorean school's philosophy, a perfect world measurable in integer ratios, was wrong. Legend has that a member of the school was drowned after showing this flaw to the outside world.
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Mar 7, 2015 07:22
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| # ¿ May 18, 2024 20:09 |
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BrigadierSensible posted:i A very historical number! (Just not a number given to dates.) The number i is fundamental to our ability to solve problems in differential equations, number theory, physics, electrical engineering, and a lot more! You might also like the quaternion numbers, which go back to 1843. The Irish mathematician Hamilton had been sitting on the idea of extra square roots of -1 for a while, but couldn't figure out how their multiplication should work*. He finally figured it out while taking a walk with his wife, and was so excited he graffitied his equations onto a bridge. Quaternions are pretty useful for modelling Newtonian physics. *The trick is that ij = -ji. Quaternions are weird.
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Mar 9, 2015 04:40
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