Euler's formula, Theorema Egregium, and Index Theory

Professor Gerardo Mendoza

Event Date
2000-10-31
Event Time
12:10 pm ~ 01:00 pm
Event Location
Student Lounge

The famous Euler's formula relates the number of vertices $V$, edges $E$ and faces $F$ in any polyhedron by a beautiful formula \[ V-E+F=2. \] For example in a cube $V=8$, $E=12$ and $F=6$, so that $8-12+6=2$. It turns out that there is a deep and mysterious connection between the Euler's theorem and another famous theorem due to Gauss. When Gauss discovered it, he was so amazed by its beauty that he called it "Theorema Egregium" ('remarkable theorem') in a very uncharacteristic for Gauss self-praise. I will explain how this connection gave rise to an extensive and important topic of current research.