Monday, July 09, 2012

The penny drops

Stolen from a place. What is the shape of a coin that has probability 1/3 of landing (and standing) on its edge?

2 comments:

RWH said...

I will guess that it's a cylinder with h = d.

Steve said...

Let's assume that the coin falls as if it were gently set up in its landing position and then released, with no kinetic or rotational energy.

When the coin with square profile (h = d) lands, the angle that the flat sides form with respect to the floor determines the way the coin falls. If the flat sides are more nearly horizontal, the coin will end up on a side; if the flat sides are more nearly vertical, the coin will end up on its edge.

These two cases occur with equal frequency, so the square profile coin will end up standing on its edge half the time.