We use video animations to explain how Hamiltonian paths, spanning trees, cosets in groups, and factor groups can be used to create computer generated symmetry patterns in hyperbolic and Euclidean planes. These methods were used to create the image for the 2003 Mathematics Awareness Month poster.

Did you know that The Simpsons and Futurama contain hundreds of humorous mathematical and scientific references? What curious mathematical object is used as a bottle for beer in the 31st century? What happens when Homer tries to emulate Thomas Edison? What is the significance of the number 1729? The only prerequisite for this talk is an open mind, so come find out!

We'll explore the mathematical content and educational value of some favorite moments along with the motivations and backgrounds of the writers during an interactive talk. Popular culture can reveal, reflect, and even shape how society views mathematics, and with careful consideration of the benefits and challenges, these programs can be an ideal source of fun ways to introduce important concepts and to reduce math anxiety. In the process we'll look at related, recent work in geometry and computational number theory so a calculator and writing utensil will be useful. For more information, check out SimpsonsMath.com and FuturamaMath.com

The unexpected discovery more than two decades ago of several new ways to distinguish mathematical knots precipitated a surge of interest in knot theory. Today, intriguing links between knots and physics and illuminating biological applications testify to the new importance of a mathematical pursuit that began in the 19th century with the search for a new atomic theory.

Artworks dating back to the invention of soap illustrate the wonder of soap bubbles and soap films. Soap bubbles have inspired not only art but also important developments in mathematics and science. Get a fresh perspective on minimal surfaces and their role in art, mathematics, science, and engineering.