Mean Diagonals

Calculus Level 2

Diagonals of a regular 30-gon Diagonals of a regular 30-gon

Let MnM_n be the arithmetic mean of the lengths of all the diagonals of the regular nn-gon with a circumradius of π\pi.

Compute limnMn\displaystyle \lim_{n \to \infty} M_n.


Image Credit: Graeme McRae.
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