SUMS: Hendriksen -- The Mathematics of Juggling

Juggling certainly seems like a non-mathematical activity.  It looks more like a test of
reflexes than anything really related to numbers.  But imagine a juggler juggling a
whole heap of balls, when suddenly he throws one really high.  In what ways can he throw
the rest of the balls so that he can be sure to have a free hand to catch the high one
when it comes back down? 

If we make a few basic assumptions about how he is juggling - like that he only catches
one ball at a time and he’s not doing anything showy like juggling behind his back or
under his legs, it turns out we can quite neatly characterise his patterns using a
simple numbering system.  After introducing the system, we’ll show a nice result or two
about the number of balls in a pattern and the types of patterns that can be done,
before moving on to construct a map of all possible juggling patterns that can be done
for a given number of balls and a maximum throw height.  The maps have some really
interesting properties that can also be investigated.  

There will definitely be practical demonstrations of the juggling involved.