I would like to calculate the mean distance depending on circle shape points,
This is a mean for calculating all possible distances between any two points
for $N=2$, line, there is only 1 distance.
for $N=3$, triangle, again, there is only 1 distance
for $N=4$, square, henceforth there are more than 1 distance.. in this case we would have four distances for sides and two distances in diagonal path, $\sqrt{2}$, then the mean distance would be
$D=(4+2\sqrt{2})/6=1.138..$
for $N=30$, it would be a "pixeled" circle .. and $N=\infty$ is a circle
How to calculate it for $N>4$ ? Is there any general formula or can it be derived?
Thanks!