Catching and Releasing: Part 1

There.s more mathematics involved in juggling than just trying to
make sure that the number of balls (or chainsaws) that hits the
ground stays at zero. Subjects such as combinatorics and abstract
algebra help jugglers answer important questions, such as whether a
particular juggling pattern can actually be juggled. For example,
can balls be juggled so that the time period that each ball stays
aloft alternates between five counts and one? The answer is Yes.
Math also tells you that the number of balls needed for such a
juggling pattern is the average of the counts, in this case three.
Once a pattern is shown to be juggleable and the number of balls
needed is known, equations of motion determine the speed with which
each ball must be thrown and the maximum height it will attain.
Obviously the harder a juggler throws, the faster and higher an
object will go. Unfortunately hang time increases proportionally to
the square root of the height, so the difficulty of keeping many
objects in the air increases very quickly. Both math and juggling
have been around for millennia yet questions still remain in both
subjects. As two juggling mathematicians wrote, .A juggler, like a
mathematician, is never finished: there is always another great
unsolved problem.