The Mathematics of JugglingAs a juggler the author likes to finish his performances with a stunt that combines props and techniques from a variety of juggling disciplines. Imagine him idling on a giraffe unicycle, while balancing a spinning basketball on a mouth stick, and toss-juggling a sword, a toilet plunger, and a rubber chicken. As a mathematician he is also interested in the treasure trove of beautiful mathematics used to model the different activities in a juggler's repertoire. In this book he provides an intellectually stimulating collection of mostly self-contained mathematical essays that introduce the reader to many elegant results and techniques from a wide range of mathematical disciplines such as combinatorics, graph theory, knot theory, mechanics, differential equations, control theory, and robotics. "The Mathematics of Juggling" is the first comprehensive account summarizing and expanding the results in the literature on juggling tricks and skills, as well as the mathematics behind these tricks and skills. Anybody who is not put off by the word "mathematics" in the title of this book should have a good time reading it. |
Contents
Preface | 1 |
Multiplex Juggling | 65 |
Multihand Juggling 85 | 84 |
Practical Juggling | 117 |
Jingling or Ringing the Changes | 141 |
Right Cosets and NoCall Principles | 173 |
Stereograms of Hamiltonian Cycles | 201 |
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Common terms and phrases
0-throws 2-hand juggling 3-ball cascade 4-bell extent arcs b-ball juggling sequences b-ball multiplex b-ball state graph beat points bells braid cascade juggled causal diagram Cayley graph change ringing Claude Shannon clubs construct contains corresponding juggling cosets cyclic shifts diagram in Figure edges elements entry Erin exactly example finite sequence fountain graph of height h hands Hamiltonian cycles height h integers inverse jugglable jugglers juggling animator juggling cards juggling diagram Juggling Information Service juggling matrices juggling pattern labeled Lewbel magic juggling sequence mathematical matrix maximal prime loop method multiplex juggling sequences multiplex state graph n-body problem necklace nonnegative integers Note number of balls orbits permutation test Plain Bob plain course prime juggling sequence principle quence result Reverse ringers ringing array robot sequences of height sequences of period simple juggling sequences spins starting swap symmetric group Table toss juggling transition sequence trick truncated octahedron uniform juggling pattern vertex vertices