Triangles in convex distance planes

Original Paper


The article deals with a plane equipped with a convex distance function. We extend the notions of equilateral and acute triangles and consider circumcenters of such triangles.


Convex distance Bisector Central set Acute 

Mathematics Subject Classification

52A10 52A21 


  1. Alonso, J., Martini, H., Spirova, M.: Minimal enclosing discs, circumcircles, and circumcenters on normed planes (Part II). Comput. Geom. 45, 350–369 (2012)MathSciNetCrossRefMATHGoogle Scholar
  2. Icking, C., Klein, R., Lê, N.-M., Ma, L.: Convex distance functions in 3-space are different. Fund. Inform. 22, 331–352 (1995)MathSciNetMATHGoogle Scholar
  3. Icking, C., Klein, R., Lê, N.-M., Ma, L., Santos, F.: On bisectors for convex distance functions in 3-space. In: Proceedings of the 11th Canadian Conference on Computational Geometry, Vancouver, pp. 291–299 (1999)Google Scholar
  4. He, C., Martini, H., Wu, S.: On bisectors for convex distance functions. Extr. Math. 28, 57–76 (2013)MathSciNetMATHGoogle Scholar
  5. Jahn, T.: Extremal radii, diameter and minimum width in generalized Minkowski spaces. Rocky Mt. J. Math. 47, 825–848 (2017)MathSciNetCrossRefMATHGoogle Scholar
  6. Jahn, T.: Successive radii and ball operators in generalized Minkowski spaces. Adv. Geom. 17, 347–354 (2017)MathSciNetCrossRefMATHGoogle Scholar
  7. Kobos, T.: An alternative proof of Petty’s theorem for for equilateral sets. Ann. Pol. Math. 109, 165–175 (2013)MathSciNetCrossRefMATHGoogle Scholar
  8. Ma, L.: Bisectors and Voronoi diagrams for convex distance functions. Dissertation, Fernuniversität Hagen (1999)Google Scholar
  9. Martini, H., Spirova, M.: Covering disks in Minkowski planes. Can. Math. Bull. 52, 424–434 (2009)CrossRefMATHGoogle Scholar
  10. Väisälä, J.: Observations on circumcenters in normed planes. Beitr. Algebra Geom. 68, 607–615 (2017)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Managing Editors 2018

Authors and Affiliations

  1. 1.Matematiikan laitos, Helsingin yliopistoHelsinkiFinland

Personalised recommendations