Archiv der Mathematik

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

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.


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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