Dr. Matthew Wright paid our students a visit this past Friday and gave them a gentle introduction to topology and the Euler Characteristic. This is a topic given little to no treatment inside the traditional K-12 math curriculum, so our students welcomed the opportunity to learn some ‘college math.’ He had our students counting vertices, edges, and faces of various surfaces in order to compute the Euler Characteristic. Students discovered that the Euler Characteristic is a topological invariant.
In his talk he also walked the students through a proof that there are only five regular surfaces, using the Euler Characteristic. This is more difficult than the typical proof, but elegant because the proof doesn’t appeal to geometry. That is, the proof doesn’t ever require the assumption that the faces, angles, or edges are congruent. In this sense, it is a topological proof.* Very cool indeed!
Bio: Matthew Wright went to Messiah College and then went on to received his MS and PhD from University of Pennsylvania, where his thesis was in applied and computational topology. He was a professor at Huntington College for two years but is now at the Institute for Mathematics and its Applications at the University of Minnesota for a postdoctoral research fellowship. His hobbies include photography and juggling. On a personal note, Matthew was my roommate in college, and I had the privilege of being his best man in his wedding, as well!
For more about Dr. Wright, visit his website at http://mrwright.org/.
* This proof also appears in the book Euler’s Gem by Dave Richeson.