The limit of such a regular ngon is a circle with radius pi.
In polar coordinates if can be plotted as
r = 2*pi*cos(theta)
I'm tempted to say that the sought mean length would be
Integral{0 to pi}(2*pi*cos(theta) d(theta) / pi
but this does not take into consideration any clustering of the angles involved; it assumes the angles the diagonals make with tangents at a given point are uniformly distributed. So I don't think it's worthwhile to use this integral.

Posted by Charlie
on 20181123 11:42:02 