I have an abstract triangulation, which consists of nodes without coordinates and connectivity information (the triangles themselves). I also know that each link has a fixed length. For simplicity we ...
Do we really need to use the Jordan-Schönflies Theorem to prove that every surface can be triangulated?
I have read that most proofs of the triangulability of surfaces require the use of the Jordan-Schönflies Theorem. However, is such high-tech machinery really needed? The problem is that 3-manifolds ...
Take a triangulation of the 2-sphere, $S^2$. Let the triangulation be denoted $T$. The Euler characteristic tells you that the number of triangles in $T$ is even. Since triangulations of the ...