Quiz!!

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**

**"Colorful Symmetries"**

**by: Brenda Forbes**

**Tuesday, September 22, 1:40 p.m.**

**in Patterson 301**

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