Sigma story [4]: Friends in high places
The year is 1807: the French army is approaching the city of Göttingen, Prussia. Napoleon, the Emperor, orders the city to be spared, because “the greatest mathematician of all times is living there”. When the French decide to charge the Germans for the generosity, Carl Friedrich Gauss, age 30, is supposed to pay a fine of 2000 francs, way above his means. Fortunately, mathematicians’ solidarity kicks in; Count Laplace pays the fine on his behalf.
In 1818 Gauss begins a geodesic survey of Hannover, the idea being to use the curvature of the earth to improve accuracy of geographic measurements; it takes him almost 30 years to finish. He notices that as the number of measurements grows they seem to cluster around a central point, and the error distribution looks like the bell curve. Sometime during this period, Gauss figures out the equation of the curve: the probability density function of the normal distribution. The equation has two variables: the mean and the sigma.
To be continued.