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How/why was the Gaussian function invented?

The function reminds me of nothing and I don't understand why Gauss would want to derive such thing, but we can see that it has numerous applications, so is there some connection between applicability and the way it's derived?

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    $\begingroup$ See the history of the normal distribution. $\endgroup$ – Rahul Feb 29 '16 at 3:23
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    $\begingroup$ If you're looking for context of the problem, Gauss had been charged with surveying Germany and was trying to deal with the problem that every time his surveyor's brought back data, they couldn't measure the same distance the same way twice. There are some good references to the history of the problem in non-rigorous reading material such as Euclid's Window if you don't mind the story telling format. $\endgroup$ – Phillip Hamilton Feb 29 '16 at 3:56
  • $\begingroup$ what I understand from wikipedia is that Laplace more than Gauss made a full definition of the normal distribution, from the experimental observations, the central limit theorem, the Fourier/Laplace transform of $e^{-x^2}$ and the differential equation $f'(x) = -2x f(x)$ $\endgroup$ – user1952009 Feb 29 '16 at 21:11
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Look at:

Saul Stahl, The Evolution of the Normal Distribution, Mathematics Magazine, Vol. 79 (2006), pp. 96-113

The paper won the Carl B. Allendoerfer Award in 2007 and can be found here

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  • $\begingroup$ Hi, shvjds. This is what we call a link-only answer, meaning that the most important information is in a link. If that link dies, the answer is useless. Can you add in the relevant information? Thanks. $\endgroup$ – HDE 226868 Mar 12 '16 at 17:15

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