There are many things which are called “elliptic” in various branches of mathematics:
- Elliptic curves
- Elliptic functions
- Elliptic geometry
- Elliptic hyperboloid
- Elliptic integral
- Elliptic modulus
- Elliptic paraboloid
- Elliptic partial differential equation
I take it that most of them relate to ellipses in one way or another, but the relation is often unclear to me. Does anyone know the etymology of these various terms; i.e. which was derived from which, and why? For example, this answer suggests that elliptic curves derive from elliptic integrals, since the first known elliptic curves were found while studying elliptic integrals. How about the rest?
I don't expect answers to exhaustively address all terms, but hope that eventually enough answers will contribute to form a cohesive picture of the whole term.