Archiv der Mathematik

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

Decomposition of closed orientable geometric surfaces into acute geodesic triangles

  • Sheng Bau
  • Stephen M. GagolaIIIEmail author


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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Eppstein, Acute square triangulations, Geometry Junkyard, computational and recreational geometry,
  2. 2.
    X. Feng, L-P. Yuan, and T. Zamfirescu, Acute triangulations of Archimedean surfaces: the truncated tetrahedron, Bull. Math. Soc. Sci. Roumanie 58 (2015), 271–282.MathSciNetzbMATHGoogle Scholar
  3. 3.
    X. Feng and L-P. Yuan, Acute triangulations of cylindrical surfaces, (to appear).Google Scholar
  4. 4.
    H. Maehara, On a proper acute triangulation of a polyhedral surface, Discrete Math. 311 (2011), 1903–1909.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    J.G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer, New York, 2006.zbMATHGoogle Scholar
  6. 6.
    L-P. Yuan, Acute triangulations of polygons, Discrete Comput. Geom. 34 (2005), 697–706.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    L-P. Yuan, Acute triangulations of pentagons, Bull. Math. Soc. Sci. Roumaine 53 (2010), 393–410.MathSciNetzbMATHGoogle Scholar
  8. 8.
    L-P. Yuan, Acute triangulations of trapezoids, Discrete Appl. Math. 158 (2010), 1121–1125.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    C.T. Zamfirescu, Survey of two-dimensional acute triangulations, Discrete Math. 313 (2013), 35–49.MathSciNetCrossRefzbMATHGoogle Scholar

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

Personalised recommendations