0

I know the function defining an n-ellipse and I know the set theory definition of all points on that n-ellipse but I haven't seen discussions of generalizing the formula of a 2-ellipse anywhere online. Is it impossible to find this integral with a finite number of functions? Is it just way too complicated and not very useful? Regardless, even if you can't figure out the exact formula, I'm very curious to know if it even exists, because I'm just taking Linear Algebra and Calc 2 and I do not have the solution to this problem.

Clarifying edit: This is for a 2-dimensional shape in which the sum of the distances from n loci to all points on the function defining that shape is all the same.

yeep-yorp
  • 53
  • @ClaudeLeibovici I'm talking about a 2-dimensional ellipse with n loci. With 1 it's a circle, and there's a very famous integral for 2, a normal ellipse, but 3 and above I haven't seen used at all. – yeep-yorp Apr 03 '23 at 05:28
  • @ClaudeLeibovici I'm not really talking about that at all. https://en.wikipedia.org/wiki/N-ellipse This is what I'm talking about. An n-ellipse doesn't really have anything to do with the concept of superellipses because it doesn't have those axes. – yeep-yorp Apr 03 '23 at 05:35
  • Now, it is clear. Thanks – Claude Leibovici Apr 03 '23 at 05:38
  • The general approach would be via: What's the arc length of an implicit function, but this would be difficult without any assumptions on the curve. At the very least, we can assume that the curve is closed, convex, and smooth. – Graviton Apr 03 '23 at 07:08

0 Answers0