Parametric Equations at the Circus: Trochoids and Poi Flowers

SummaryPoi spinning is a performance art, related to juggling, where weights on the ends of short chains are swung to make interesting patterns. We study a certain class of moves for poi where the patterns created are centered trochoids. Like all curves in the cycloid family, they are best expressed using parametric equations. Using the calculus of the curves, we find that there are just a few places where one pattern can be smoothly transformed into another.