DMS Graduate Student Seminar

Speaker: Professor Andras Bezdek 

Title:  Euler's theorem and its various, mostly geometric, proofs

Abstract: Euler’s formula states that if a finite, connected planar graph is drawn in the plane without any edge intersections, and v is the number of vertices, e is the number of edges and f is the number of faces (regions bounded by edges, including the outer, infinitely large region), then v-e+f =2. 

The 3D version of Euler’s formula says that the same equation holds for the edge graph of convex polyhedra. 

There are over 14 proofs for the above two variants. The following students, as part of a class project (MH7110), prepared a zoom video for the graduate students seminar. I hope you will enjoy their presentation and can review these educationally very important proofs, even if you already read, maybe even several times, some of them. 

The following students will present: 

Dual electric charge proof (Yida Bao, Alejandra Brewer Castano) 

Noah’s Ark proof (Jared Deleo, Rachel Galindo, Padmini Naukala)

Speherical Angle proof (Sean Grate, Josey Graves) 

Proof by induction (Devin Hensley, Evan Leonard) 

Divide and Conquer proof (Shayne Richardson, Roman Vasquez)