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
No comments:
Post a Comment