Steve Butler

Iowa State University

Juggling Counts

Mathematics is a language which can help us describe and explore patterns. One source of patterns that mathematicians have been exploring comes from juggling (the tossing of objects, usually balls or clubs). In this talk we will look at multiple ways to describe juggling patterns that allow us to find new juggling patterns, and to count how many possible patterns exist. We can compare answers to various problems to give a combinatorial proof of Worpitzky's identity.  We will also look at a few juggling-based problems that mathematics has not yet succeeded in answering.