Jugglings

Ball Passing Patterns

This page collects many two-person passing patterns, performed by Alice and Bob. I hope you can understand my diagrams. In doubt you can try to find explanations on my page about the mathematical theory of juggling.

I only consider the part of the passing pattern which can be described by some kind of site-swap notation. The basic version for these patterns is to stand front-to-front and to do the indicated throws. But of course all of these patterns can be enhanced by doing throws under your leg, from behind your back, by doing a mills' mess while performing the pattern, or by standing back-to-back.

The Mathematical Theory of Juggling

The purpose of this text is to explain enough of the theory of juggling, that you can understand the juggling patterns which are explained on my juggling web pages. This page does not intend to give a complete explanation of site-swaps and indeed there are many interesting facts omitted. If you want to know more, Burkhard Polster's book The Mathematics of Juggling is a good reference. The references section below also contains some links to online resources.

The Physics of Ball Juggling

The purpose of this text is to explain some physical background of ball juggling. While the number of hands and the timing of throws is abstracted away in the mathematical theory of juggling, these quantities play a central role in this text.

The present version of the text is work in progress and will hopefully be extended.

The Timing of Throws

In this section we will have a look at a real-world juggling pattern to see what is going on. We will get timing information from the pattern, derive Shannon's first theorem about juggling, and finish this section by exploring how fast or slow you can juggle while keeping the same height of throws.

Juggling Patterns

This page collects several juggling patterns, which can be described as site-swaps. This is a restriction which leads to the omission of many great juggling patterns like the Mills' Mess and of many tricks like throwing behind your back. But, as you will see, even with this restriction in place there is some interesting stuff left.

Basic Three Ball Patterns

three-ball cascase

four-four-one

three-ball shower

Advanced Three Ball Patterns

five-three-one

four-five-zero

Four-ball patterns

four-ball fountain

four-ball half-shower

four-ball tennis

four-ball shower