As mathematicians are in the habit of doing, we start by throwing
away irrelevant detail.
In a juggling pattern we will ignore how many people or hands
are involved, ignore which objects are being used, and ignore
the specific paths of the thrown objects. We will assume
that there are a fixed number of objects (occasionally referred to
as ``balls'' for convenience) and will pay attention only to the times
at which they are thrown, and will assume that the throw times are
periodic.
Although much of the interest of actual juggling comes from peculiar
throws (behind the back, off the head, etc.), peculiar objects
(clubs, calculus texts, chain saws, etc.), and peculiar
rhythms, we will find that the above idealization is sufficiently
interesting.
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