The Doctrine of Chances


Binomial expansion

(de Moivre, 1756, p.257)

De Moivre noticed a remarkable fact about these normalized coefficients, namely, that if we scale the normalized coefficients by the square root of m, and scale the indices by the reciprocal of this square root, all the coefficients appear to lie on (or very close to) a single curve. []

de Moivre, A. (1756). The doctrine of chances: or, A method of calculating the probabilities of events in play. London: Printed for A. Millar, in the Strand. [link]