In 1602, Galileo Galilei became interested in studying the motion of a swinging lamp at a church in Pisa. His studies, along with the invention of the Integral Calculus, led to the introduction of elliptic integrals. In 1718, Count Giulio Fagnano found a curious “duplication formula” by considering a point on a curve called the lemniscate (“pendant ribbon”). These results were subsequently generalized by Leonhard Euler in 1728 to a larger set of curves. Eventually this led to a theory of “elliptic curves”. In this presentation, we give the history and genesis of the subject, culminating with the result that the set of complex points on an elliptic curve form a torus.
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