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The “Dzhanibekov effect” - an exercise in mechanics or fiction? Explain mathematically a video from a space station
That was great exposition; here is a nice video of the oscillation described: youtube.com/watch?NR=1&v=LR5hkgfRPno |
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accepted | Why is the Gaussian so pervasive in mathematics? |
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Why is the Gaussian so pervasive in mathematics?
Makes sense, thanks for that explantation about spheres. A thought: there seems to be some similarity between the formulation of the heat equation as the limit of squares with heat flow through its edges proportional to the difference of temperature and the dropping balls through pegs by relating balls to heat flow. Maybe instead of thinking of the ball as going one way or another when meeting a peg, we can consider its expectation of going either way which would be closer to the heat flow model. |
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Ingenuity in mathematics
I think an analogous proof that can be explained to artists is to tile the rectangle w/ a black and white checkerboard parallel to the rectangles with squares of width 1/2. You can then show that a rectangle having equal black and white areas (of overlapped checkerboard squares) is necessary and sufficient for determining that it has an integral side. Each rectangle with integral sides then has equal black and white squares, which combine to show that the large rectangle has the same property and thus an integral side itself. |
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Why is the Gaussian so pervasive in mathematics?
Thanks for all the comments and nice examples. Another one of my very favorite uses of the Gaussian is to find the volume of the n-sphere planetmath.org/… but its appearance here seems to have more to do with the calculation got "factored" than some especially deep fact about spheres. Is there some obvious relation between the CLT and the heat equation? (I know that the Fourier transform gives 2 matching ODEs in those two scenarios, but is there some less heavy handed explanation?) |
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Why is the Gaussian so pervasive in mathematics?
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