Archiv der Mathematik

, Volume 110, Issue 1, pp 81–89 | Cite as

Decomposition of closed orientable geometric surfaces into acute geodesic triangles

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Abstract

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.

Keywords

Acute Decomposition Geodesic Orientable Surface Triangle 

Mathematics Subject Classification

53A05 51H25 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics, Statistics and Computer ScienceUniversity of Kwazulu NatalPietermaritzburgSouth Africa
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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