Toss juggling requires more balls than hands.[3] Thus tricks such as the one ball cascade toss back and forth, 300,[4] for example, may not be considered valid patterns. Throws back and forth shower style, odd numbers, are the most common one prop practice. Invalid or practice patterns and tricks are marked with an X.
*: Synchronous pattern that switches sides. (4,2x)(2x,4) = (4,2x)*
x: Toss to the other hand during a synchronous pattern.
Asynchronous
Animations
531
Cascade: 5
Cascade: 7
A pattern is symmetrical (S) if both hands play the same role and asymmetrical (A) if not. All asynchronous patterns whose periods are odd are symmetrical, and all asynchronous patterns whose periods are even are asymmetrical.
A pattern is symmetric if all throws made by the right hand are made by the left hand in the same order. It follows that a synchronous pattern is symmetric if the sequence of throws made by one hand in the siteswap notation is a rotation of the other.
^For example, ""1. What is juggling?", IJDb". Archived from the original on December 1, 2008. Retrieved 2016-11-06.{{cite web}}: CS1 maint: bot: original URL status unknown (link). Cited in Rosenberger, Phillip (2011). Juggling Basics, Why and How To. ISBN9780983339700.
^ abcdBuhler, Joe; Graham, Ron (2004). "Juggling Patterns, Passing, and Posets". In Hayes, David F.; Shubin, Tatiana (eds.). Mathematical Adventures for Students and Amateurs. The Mathematical Association of America. pp. 100–1. ISBN0-88385-548-8. Retrieved February 17, 2011.
^"Three Ball Gap", Adian's Juggling Page. Accessed November 3, 2016.
^ abcdefghijklmnopqrstBorwein, Jonathan M.; ed. (1997). Buhler, Eisenbud, Graham, Wright. "Juggling Drops and Descents", Organic Mathematics: Proceedings of the Organic Mathematics Workshop, December 12–14, 1995, Simon Fraser University, Burnaby, British Columbia, p.141-2. American Mathematical Soc. ISBN9780821806685.
^Diaconis, Persi and Graham, Ron (2011). Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks, p.144. Princeton University. ISBN9781400839384. "Mathematically interesting siteswap patterns, such as 123456789."
^Besmehn, Bobby (1994). Juggling Step-by-Step, p.65. "Use four balls of one color and two of another color...every time an odd-colored ball reaches your right hand, pass it." Sterling. ISBN0-8069-0815-7
^Cassidy, John and Rimbeaux, B.C. (1988). Juggling for the Complete Klutz, p.38. "It helps...if one of you counts out loud every time a toss leaves your right hand[s]...On a pre-arranged number, say three [six beats], instead of tossing across to your own left hand, throw your bag...over to your friend's left hand." Klutz Press. Third edition. ISBN0-932592-00-7
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