Type: Seminar

Distribution: World

Expiry: 18 Oct 2012

Auth: gilesg@bari.maths.usyd.edu.au

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.