09-22-2007, 10:46 PM
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FFR Player
Join Date: Jun 2007
Age: 37
Posts: 40
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Elegant Mathematics
Post your favorite mathematical proof or theorem.
Mine has to be Euler's. g(x) is defined as e^ix therefore g'(x) = ie^ix, and g''(x) = -e^ix g''(x) = -g(x) g''(x) + g(x) = 0 g1(x) = cosx g2(x) = sinx g(0) = A = 1 g'(0) = B = i g(x) = e^ix = cosx + isinx And for x=pi g(pi) = e^(i*pi) + 1 = 0 The Taylor series proof and Calc proof are equally elegant. |
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