All these cases where the circle constant would naturally appear, but it accidentally gets placed next to a semi- (a [tex]\frac{1}{2}[/tex]) that comes from somewhere else, and some joker pops up and says, "See! We've got a semi-circle here folks!" and then he hits it with a [tex]\pi[/tex] in the face ... they're mathematical puns.

[tex]\pi[/tex] stands for pun.