1. How many ways can you paint your fingernails with three different colors?
2. How many ways are there to color a disk divided into three equal parts with one of two colors per section?
3. How many ways can you color an icosahedron with one of n colors per face?
Asking simple questions that are difficult to answer is common in mathematics. The first question seems pretty straight forward. Yet the second requires a bit more understanding, one of basic geometry, group theory and combinatorics.
Using Burnside’s Lemma, sometimes, called the orbit-counting theorem, we will explore this question and others like it, considering the much needed rotation of an object, looking at it from all sides.
By solving a much simpler problem, we will build to the question of the icosahedron, showing with the proper ‘tools’, the problem-solving approach needed is not that hard after all.
Bargh, B. Chase, J. Wright, M. (2014). Colorful Symmetries. Math Horizons, April 2014, pp 14-17
Math 450 Senior Seminar Presents
by: Brenda Forbes
Tuesday, September 22, 1:40 p.m.
in Patterson 301