Category Archives: Topology

The discrete Gauss-Bonnet theorem

Posted on 21/06/2016 by KKK

This is a slight extension of my previous note on discrete Gauss-Bonnet theorem. As mentioned in that note, this is a generalization of the well-known fact that the sum of the exterior angles of a polygon is always , which … Continue reading →

Posted in Calculus, Combinatorics, Discrete Mathematics, Geometry, Topology | Leave a comment

Topological proof of the infinitude of primes

Posted on 28/12/2011 by HL

Perhaps everyone knows how to prove “there exist infinitely many primes” by one or more ways. Here I just want to share a proof using topology and prime factorization theorem. It is also (perhaps highly) possible that most of the … Continue reading →

Posted in Number Theory, Topology | 2 Comments

Sum of angle defects of polyhedrons

Posted on 13/08/2011 by KKK

In this short note we will discuss a generalization of the well-known fact that the sum of the exterior angles of a polygon is always , which can also be regarded as a very special case of the Gauss-Bonnet theorem. … Continue reading →

Posted in Geometry, Topology | 1 Comment