South End Dining Hall
March 20, 2018
11:30 AM to 12:20 PM
Kristin Camenga, Juniata College (and former Houghton professor)
Making the Most of Euler's Formula
Most people remember working with polyhedra in elementary and high school: cubes, prisms, tetrahedra, pyramids, etc. Euler's formula states that if V is the number of vertices, E the number of edges and F the number of faces of a polyhedron, V + F = E + 2.
This is a beautiful and useful formula - but can't we do more? Can we get a similar theorem if we change some of our hypotheses? How does Euler's formula change if we allow polyhedra to be in dimension 4 or 5? or n dimensions? What if we look at angles of polyhedra instead of the number of faces? We will look at several examples as we generalize Euler's formula in these directions and others. We will end with a glimpse of open questions. No specific math background will be assumed, but curiosity is expected!
Science & Math Colloquium