Can you answer chadlupkes's question about degrees?:

This question came to me at breakfast this morning.

A restaurant has square napkins and several different glasses, each with different shapes for the bottom of the glass. These shapes are 4 sided, 5 sided or 6 sided. When people take a drink, and put the glasses down on the napkin, they land with the sides at a random angle to the sides of the napkin.

For each glass, what is the average number of degrees that the glass must be turned in order to bring one of the sides of the bottom of the glass in parallel with the closest side of the napkin? How do those number of degrees change with the different glasses? If you plot out those changes on a graph, and then project out for glasses with 7, 8, 9 or higher numbers of sides, how does the graph look?

Online PHD Degrees