The Mathematics of Juggling by Burkard Polster

Next time you see some jugglers practising in a park, ask them whether they like mathematics. Chances are, they do. In fact, a lot of mathematically wired people would agree that juggling is “cool” and most younger mathematicians, physicists, computer scientists, engineers, etc. will at least have given juggling three balls a go at some point in their lives. I myself also belong to this category and, although I am only speaking for myself, I am sure that many serious mathematical jugglers would agree that the satisfaction they get out of mastering a fancy juggling pattern is very similar to that of seeing a beautiful equation, or proof of a theorem click into place. Given this fascination with juggling, it is probably not surprising that mathematical jugglers have investigated what mathematics can be found in juggling. But before we embark on a tour of the mathematics of juggling, here is a little bit of a history.