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The elliptic parameterization of cubic curves by Alfred Clebsch. (Le paramétrage elliptique des courbes cubiques par Alfred Clebsch.) (French. English summary) Zbl 1403.01013

Alfred Clebsch (1833–1872) is one of the great algebraic geometers of the 19th century. Since his results are written in a language that only a select few can still read, Clebsch’s name is perhaps not as well known as it should be. In this excellent and very informative article, the author explains Clebsch’s result that nonsingular cubic curves can be parametrized by elliptic functions, which Clebsch needed for proving a theorem that Jacob Steiner had stated without proof. Connections with earlier results by Jacobi and Aronhold on Poncelet’s closure theorem are also discussed in detail.

MSC:

01A55 History of mathematics in the 19th century
11-03 History of number theory
14-03 History of algebraic geometry
14H52 Elliptic curves
33-03 History of special functions
33E05 Elliptic functions and integrals

Biographic References:

Clebsch, Alfred