4 Nov
2017
4 Nov
'17
10:32 a.m.
Given two parallelograms A,B in the plane and a translation vector v, let P(v) be the intersection of A+v with B. If we choose a random v such that P(v) is nonempty, how many sides on average do we expect P(v) to have? The set of such vectors v is a compact subset of R^2, so it's clear what probability measure to use: ordinary Lebesgue measure, rescaled. There is a nice answer to my question and at least one nice proof. I'll be curious to see proofs different from the one I found. I'm happy to answer requests for clarification, but no spoilers till Sunday, please. Jim Propp