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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