Not sure if this is the right place for this, but as I was feeling crafty the other night I wanted to put strips of colored paper on a styrofoam sphere to cover it, in the style of a beach ball. Naturally the question came up of how should the strips be cut? The strips' shape is that of the intersection of two circles, but making them is tricky. I worked out algebraically, given the diameter of the sphere and the number of strips, what diameter and how far apart the circles should be, but it was messy and required a calculator and ruler. I was hoping for something elegant and Euclidian. So then:
Given a sphere split up into n strips, can one draw one of the strips using only a compass and straight edge? Assume one can put the compass to the diameter sphere easily.