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===Siteswap===
{{Main|Siteswap}}
Developed by mathematically inclined jugglers Bengt Magnusson and [[Bruce Boppo Tiemann]] in 1985,<ref name=newsci/><ref name=nyt>{{cite news|last=Donahue |first=Bill |url=http://www.nytimes.com/1996/04/16/science/jugglers-now-juggle-numbers-to-compute-new-tricks-for-ancient-art.html |title=Jugglers Now Juggle Numbers to Compute New Tricks for Ancient Art |publisher=[[The New York Times Company]] |work=[[The New York Times]] |date=1996-04-16 |accessdate=August 29, 2009}}</ref><ref name=maa>{{cite web|url=http://www.maa.org/reviews/mathjuggling.html |title=Read This: The Mathematics of Juggling |publisher=[[Mathematical Association of America]] |date=2003-12-03 |accessdate=August 29, 2009}}{{dead link|date=October 18 2016}}</ref> [[siteswap]] is by far the most common juggling notation.
A given juggling pattern is represented by a sequence of digits, like "333", "97531", or "744". Each digit represents the number of throws that occur by the time that same prop will be caught. For example, "333" represents a common three-ball [[cascade (juggling)|cascade]], where three props are thrown before the same prop will be caught and thrown again. Within the "531531" pattern, the prop thrown first, the '5' throw, will not be caught until five throws have been made, including itself, where it will be thrown again as a '1'. The prop thrown next, the '3', will be thrown again on the third throw afterwards, the next '3'. And the next prop is thrown with a '1' throw, which is a direct pass to the other hand and will be thrown on the very next throw as a '5'.
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