Decomposition of closed orientable geometric surfaces into acute geodesic triangles
We prove that for every \(g\ge 2\), a differentiable closed orientable geometric surface of genus g may be decomposed into \(16g-16\) acute geodesic triangles. We also determine the number of acute geodesic triangles needed for the sphere and the torus.
KeywordsAcute Decomposition Geodesic Orientable Surface Triangle
Mathematics Subject Classification53A05 51H25
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- 1.D. Eppstein, Acute square triangulations, Geometry Junkyard, computational and recreational geometry, http://www.ics.uci.edu/eppstein/junkyard/acute-square
- 3.X. Feng and L-P. Yuan, Acute triangulations of cylindrical surfaces, (to appear).Google Scholar