"I am just beginning to learn about elliptic functions. Wikipedia defines an elliptic function as a function which is meromorphic on C, and for which there exist two non-zero complex numbers ω1 and ω2, with ω1ω2∉R, which satisfy f(z)=f(z+ω1)=f(z+ω2).
That's all fine and dandy, but what does this have to do with an ellipse?
I sort of know (but not really) about the Jacobi elliptic functions. I am told by the internet that the Jacobi elliptic functions can be defined as inverses of elliptic integrals, which relate to the arc lengths of ellipses. But other than that, I have no idea how elliptic functions relate to ellipses.
I have looked at several sources, like this, this, and this. From what I can understand, any elliptic function can be expressed in terms of the Jacobi elliptic functions and Weierstrass elliptic functions, but I have yet to understand why that is true. Perhaps it has something to do with what ODE's elliptic functions satisfy?
