Four Ball Juggling by Martin Probert

Juggling: From Simple Patterns To Advanced Theory
Original and entertaining material for beginner and expert
Over 700 illustrations, 202 pages, ISBN 0-9524860-0-8

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How many juggling patterns are in the book?

Notes for Technical Jugglers

Four Ball Juggling has been written to appeal to all types of juggler, the beginner, the expert juggler, and the juggler with a liking for the mathematics and theory of juggling. These notes are for the latter.

Four Ball Juggling contains much original material on juggling theory and the mathematics of juggling. This theory applies not just to four balls but to any number of balls. Those not interested in technical matters can simply ignore these parts of the book.

The technical material includes:

  • A juggling notation which extends to multiplex juggling (more than one ball thrown from a hand) and to synchronous juggling (the hands throw together). For example, the Four Ball Fountain is given by
       { R L }
       ( 4 4 }
       { f f }
  • Several elegant and simple methods of generating juggling patterns which require neither computer nor complex arithmetic. (Original to the book).
  • A notation describing the state of a pattern at any instant while being juggled. (Original to the book).
  • State Tables which enable the visual analysis of patterns and combinations. State Tables are given not only for 4 balls but also for 0, 1, 2, 3, 5, 6 and 7 balls. (Original to the book).
  • A classification of patterns into 'Low State' and 'Higher State' patterns. (Original to the book).
  • A juggling formula to relate the states before and after a throw to the throw made. (Original to the book).
  • A generalisation of the last formula to multiplex and synchronous patterns. (Original to the book).
  • An upper bound for the length of a juggling pattern. (Original to the book).
  • A method for generating multiplex patterns. (Original to the book).
  • A method for generating synchronous patterns. (Original to the book).
  • A BASIC program for generating 'Low State' patterns and combinations. (Original to the book).
  • A parallel with change ringing on peals of bells. (Original to the book).
  • How to embed patterns one within another. (Original to the book).
  • Juggletoons - an explanation of the construction of a juggling diagram that can be animated to show the movements of the balls. (Original to the book).
  • A matrix description of juggling events. (Original to the book).

For more information take a look at the contents

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