Math Day - Thursday, March 21, 2013

AMU Multipurpose Room, The University of Findlay Campus 

10:00 a.m. "The Mathematics of Juggling"

In the 1980s, several jugglers independently devised a method for representing juggling patterns using lists of whole numbers. These lists, called "siteswaps," have led to a great number of mathematical questions.  Not all lists produce valid siteswaps and we will discuss how to distinguish the legal ones from the imposters.  From a juggler's perspective, the ability to quickly generate siteswaps is valuable for performance reasons, and we will discuss methods for doing this.

1:00 p.m. "Deconstructing the Towers of Hanoi"

The Towers of Hanoi is a 130-year-old puzzle purportedly invented by the mathematician Edouard Lucas.  The brainteaser consists of a number of disks, all of different sizes and three pegs on which the disks rest. The disks are stacked on a single peg according to size with the largest on the bottom. The solver is allowed to move one disk at a time from a peg to any other provided that a larger disk is never placed on a smaller one.  The goal of the puzzle is to move the entire stack of disks to another peg, preferably with the fewest possible moves.  We will discuss how to solve the puzzle and will discover the formula for the minimum number of moves.  We will also look at some surprising connections between the puzzle and other areas of mathematics, including geometry and number theory.