Part 1
Determine the mean distance between two random points on the perimeter of a unit (convex) regular hexagon.
Part 2
Determine the mean distance between two random points on the interior of a unit (convex) regular hexagon.
(In reply to
re: comment by Brian Smith)
I take your point. All points on a perimeter being equal and all points in an interior being equal does indeed in each case lead to a uniform distribution from which to draw two points. (Although, note, in the video link, there is the question raised at the end as to whether specifying four random points on a spherical surface is an unambiguous task.)
Bertrand's paradox comes more into play when requiring a random chord across a shape. The ambiguity is removed if the prescription to draw the chord is given: e.g, "first pick two random points within the shape."
Edited on October 14, 2022, 5:13 pm
re(2): comment
