The Gauss-Bonnet theorem tells us that for a particular manifold this quantity is proportional to th
The Gauss-Bonnet theorem tells us that for a particular manifold this quantity is proportional to the integral of Gaussian Curvature. More generally it can be defined as the alternating sum of the ranks of corresponding homology groups, which are known as the Betti Numbers. Equal to 0 for the Torus and Klein bottle, this is-- for 10 points-- which mathematical quantity defined as Vertices minus Edges plus Faces, and named for a prolific Swiss Mathematician.
The Gauss-Bonnet theorem tells us that for a particular manifold this quantity is proportional to the integral of Gaussian Curvature.
Euler Characteristic