Creating a fair 3 sided coin I want to make a cylindrical three sided fair coin, with sides: heads, tails, and edge.
What should the area of the edge be in relation to the area of the head of the coin?
Assume it is all made of a uniform material.
Thoughts: I was thinking that so long as the surface areas of all three sides were equal, that would be enough, but this seems to lead to tipping over and landing on one of the other faces. Another thought was that the height of the edge should be equal to the diameter of the face, but this seems much too thick.
I am looking for a rigorous way of approaching the problem, as opposed to using (bad?) intuition.
 A: Seriously, by far the easiest way is to find it empirically. Take several coins and find the number of coins it is required to make a fair one by piling them together. The problem seems to be hard from the theoretical point of view.
However, a bit of googling in google scholar brought out "Probability and dynamics in the toss of a non-bouncing thick coin". The abstract says:

When a thick cylindrical coin is tossed in the air and lands without
  bouncing on an inelastic substrate, it ends up on its face or its
  side. We account for the rigid body dynamics of spin and precession
  and calculate the probability distribution of heads, tails, and sides
  for a thick coin as a function of its dimensions and the distribution
  of its initial conditions. Our theory yields a simple expression for
  the aspect ratio of homogeneous coins with a prescribed frequency of
  heads/tails compared to sides, which we validate by tossing
  experiments using coins of different aspect ratios.

As you see "without bouncing on an inelastic substrate" is not a very realistic assumption, so empirical approach would still be better. Nevertheless, I recommend you to read the article, I didn't, but I think there should be quite a lot of useful information.
