# A discrete Gauss-Bonnet type theorem

```@article{Knill2010ADG,
title={A discrete Gauss-Bonnet type theorem},
author={Oliver Knill},
journal={arXiv: General Topology},
year={2010}
}```
• O. Knill
• Published 2010
• Mathematics
• arXiv: General Topology
We prove a prototype curvature theorem for subgraphs G of the flat triangular tesselation which play the analogue of "domains" in two dimensional Euclidean space: The Pusieux curvature K(p) = 2|S1(p)| - |S2(p)| is equal to 12 times the Euler characteristic when summed over the boundary of G. Here |S1(p)| is the arc length of the unit sphere of p and |S2(p)| is the arc length of the sphere of radius 2. This curvature 12 formula is discrete Gauss-Bonnet formula or Hopf Umlaufsatz. The curvature… Expand
37 Citations
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• ArXiv
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• ArXiv
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• 2015
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