# Toss juggling

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Toss juggling is the most familiar form of juggling to most people. Objects – typically balls, clubs, or rings – are repeatedly thrown and caught in a variety of different patterns and styles.

The term "toss juggling" is only used by a very small subset of jugglers referring to "pure juggling" (throwing and catching juggling) in contrast to the wider range of circus skills usually associated with the term "juggling", such as diabolo, devilstick, cigar boxes, etc.

## Patterns

The simplest form of toss juggling is the three-ball pattern cascade. Most jugglers learn this as their first pattern. The balls are thrown with alternating hands; the left hand throws from the left side to the right side and the right hand vice versa. When the ball from the left hand is at its topmost position, the right hand comes into play.

The cascade pattern is extendable to any odd number of objects; the only thing that changes is the frequency at which the balls have to be thrown. Usually the height of the pattern increases with an increasing number of balls, as a larger pattern allows a slower frequency.

For even numbers of objects, juggling in a cascade pattern is not possible continuously. The most basic pattern for even numbers is the fountain, throwing balls from the center to the outside on the same side. Basically, each hand juggles half the objects in a circle.

In a shower pattern, one hand does high throws, while the other hand catches and hands the objects across. Although much harder to juggle than a cascade or a fountain, this pattern is very simple to understand and is usually the pattern laymen assume is the standard pattern.

## Multiple Jugglers

In addition to juggling by themselves, many jugglers enjoy passing: juggling that involves throwing to others. This leads to a whole new host of patterns, ranging from two cascade patterns with an occasional exchange to "ultimate" patterns with no object being caught by the thrower. In addition to the objects' motion in time, passing also allows for different positions of the jugglers. With more than two jugglers, intricate "runaround" patterns require the jugglers to walk around while passing.

Interaction between jugglers does not require all of them to juggle. Another common form is the sharing of patterns - one juggler starts a pattern, and another takes over while the objects are in the air. Takeouts involve stealing clubs from someones pattern and filling the gap with a different club. Takeouts in passing patterns can be particularly interesting, as the gap can move to a different juggler in the meantime. Advanced takeout patterns may also involve changing roles fluidly.

## Notation

To communicate and remember patterns, several forms of juggling notation have been developed. Diagrammatic notations are intuitive, but require something to draw on. In many cases, text notations are favored over a diagram. Although no text notation is as general as a diagram can be, it is always easier to use in spoken and written language.

There are two main ways to depict juggling in a diagram. A ladder diagram is simply a graph of the objects' location in a horizontal direction vs. time. The hands are depicted as straight lines, their location being almost constant in time, with the objects going back and forth. Ladder diagrams quickly become cluttered, especially when dealing with several interacting jugglers at one. Causal diagrams remedy this by only drawing the objects in the air, not all objects at every point in time. Thus, only "problems" - objects approaching filled hands - are shown, and the diagram shows one problem causing the next.

The most widespread text notation for juggling today is siteswap. It assumes all hands throw alternately, one object at a time, and uses numbers to indicate how many beats later the object is to be thrown again. Knowing the order of hands, one can then work out which hand the object gets thrown to, and how high to throw it in order to allow for all the beats until the object is next thrown. Siteswap was developed in 1985 and has been extensively studied [1]. It is related to mathematical Graph Theory.

There are several extensions to the simplest form of siteswap described above, allowing for multiplexes (more than one object thrown at once), hands throwing synchronously and passing with other jugglers.

A relatively new notation, beatmap, uses a slightly different approach. All hands are noted on every beat, allowing for more accurate description of dwell times and easier accommodation of additional manipulators (for example a foot kicking an object into the pattern).

## References

1. Buhler, Joe, Eisenbud, David, and Wright, Colin (1994). "Juggling Drops and Descents", American Mathematical Monthly, Vol. 101, No. 6. (Jun. - Jul.), pp. 507-519.