So you've learned to juggle 3 or 4 balls, but 5 is way too difficult and you've run out
of tricks to learn. Now what? It's math to the rescue. After seeing that juggling
patterns are functions on the integers with certain properties, we encode them as
sequences (known as Site Swap notation). This gives us many new juggling patterns to
learn. It also opens up all kinds of questions, such as: What sequences constitute
juggling patterns? How can one generate all the juggling sequences? How many juggling
sequences are there, say, of length $l$ using $b$ balls? (Some of these questions will be
answered.)