Mean Diagonals

Calculus Level 3

Diagonals of a regular 30-gon

Diagonals of a regular 30-gon

Let \(M_n\) be the arithmetic mean of the lengths of all the diagonals of the regular \(n\)-gon with a circumradius of \(\pi\).

Compute \(\displaystyle \lim_{n \to \infty} M_n\).


Image Credit: Graeme McRae.
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