Did Christians actually debate how many angels can dance on the head of a pin?

I've heard references to debates about how many angels can dance on the head of a pin, and it's always been presented as a pointless exercise. If such debates have actually occurred, presumably the participants didn't see them as pointless and thought there was both a way to answer the question and a reason to do so. Did these debates actually occur, and if so what were the reasons at the time? (For bonus points, what answers did people give and was there ever anything approaching consensus?)