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.
Reviewer: Franz Lemmermeyer (Jagstzell)
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 |