Let E be a bounded, closed set of infinitely many points in the plane. Define the separation of a (possibly concave) polygon as the geometric mean of the lengths of all of its diagonals and edges. For each integer n > 2 let s_{n} be the maximum possible separation of an n-gon with vertices in E.

Prove that lim n -> ∞ s_{n} exists.

Prove that lim n -> ∞ s_{n} exists.

Original post by Arya desai

Let E be a bounded, closed set of infinitely many points in the plane. Define the separation of a (possibly concave) polygon as the geometric mean of the lengths of all of its diagonals and edges. For each integer n > 2 let s_{n} be the maximum possible separation of an n-gon with vertices in E.

Prove that lim n -> ∞ s_{n} exists.

Prove that lim n -> ∞ s_{n} exists.

Out of interest, where is the problem from?

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can someone please explain what principle domain is and why the answer is a not c?Maths

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