Etymology, history, and artifacts
نویسنده
چکیده
Elliptic really does have a connection with literal geometric ellipses, removed by a few steps. Integrals expressing arc length of ellipses are less elementary than integrals for inverse trigonometric functions, and were named elliptic because of this. Abel and Jacobi discovered in 1827 that the inverse functions are doubly periodic (explained below). This chain of events caused these functions to be called elliptic functions, which does not at all suggest that they are doubly periodic. Further, for a fixed periodicity lattice, the elliptic functions for that lattice satisfy algebraic relations. The basic relation is of the form (found by Weierstraß)
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