Oct 9, 2022 · The ladder diagram of a juggling pattern keeps track of where each ball is throughout time. The x-axis is time, the y-axis is position between the left and right hands.

To get you started, I particularly recommend Juggling Lab by Jack Boyce, arguably the most powerful and useful simulator for mathematical juggling involving just one juggler.

In this paper we examine a simple method of describing juggling patterns using mathematical notation, and then use this notation to predict new juggling patterns.

Multihand Juggling 4.1 Juggling Matrices 4.2 Average Theorem and Permutation Test 4.3 Multihand State Graphs 4.4 Operations Involving Juggling Matrices

We also show how to enumerate σ-juggling sequences and primitive σ-juggling sequences with period n. As we will see, one use of primitive juggling sequences is that we can make new juggling sequences …

Subjects such as combinatorics and abstract algebra help jugglers answer important ques-tions, such as whether a particular juggling pattern can actually be juggled.

Juggling involves mathematics in at least 2 ways. Firstly, there are variable forces (hence accelerations) acting on juggled objects, exerted by the juggler (who can produce forces in any direction).