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Remarks for Jugglers Only
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The above description is geared towards the standard model:
two hands throwing alternately, in constant rhythm.
In fact there could be any number of hands and it is
not necessary to assume that the rhythm is constant.
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The practical meaning of the throw heights 0, 1, and 2 in the
standard model requires a little thought.
A throw height of 0 corresponds to an empty hand.
A throw height of 1 corresponds to a rapid shower pass from
one hand to another that is thrown again immediately.
A throw height of 2 would ordinarily
indicate a very low throw from a hand to itself that is thrown
again by that hand immediately. This is actually rather
unnatural in practice; the conventional interpretation
([11], [12]) is that a throw height
of 2 is a held ball.
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The paradigm for categorizing juggling patterns here is very interesting in
practice, although many of the patterns require considerable
proficiency. Several jugglers who have spent time in working on site swaps
describe the same gain in flexibility and conceptual power that
mathematicians seem to report from the use of well-chosen abstractions.
The simplest non-obvious site-swap seems to be 441; it is similar to,
but not the same as, the common 3-ball pattern of throwing balls up
on the side while passing a ball back and forth underneath in a shower
pass from hand to hand. (The latter pattern is not commonly performed with
an even rhythm; if it is, it is 810.)
The 3-ball 45141 pattern is also amusing, and the 4-ball
5551 pattern looks very much like the 5-ball cascade.
The range of feasible and interesting tricks seems to be
unlimited; we mention the following sample:
234, 504, 345, 5551, 40141,
561, 633, 55514, 7562, 7531, 566151, 561, 663, 771, 744, 753, 426, 459, 9559,
831.
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A number of programs are available that
simulate site swaps on a computer screen, sometimes with quite
impressive graphics. These programs take a finite
sequence of non-negative integers as input and dynamically represent the
pattern.
The Internet news group rec.juggling is a source of information
on site swaps and various juggling animation software.
A juggling site is here.
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Next: Counting Periodic Juggling
Up: Periodic Juggling
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