Euler’s ratio-sum formula in projective-metric spaces

  • Árpád KurusaEmail author
  • József Kozma
Original Paper


We prove that Euler’s ratio-sum formula is valid in a projective-metric space if and only if it is either elliptic, hyperbolic, or Minkowskian.


Projective metrics Hilbert geometry Minkowski geometry Ellipses Triangles Tangential ratio 

Mathematics Subject Classification

53A35 51M09, 52A20 


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Copyright information

© The Managing Editors 2018

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary
  2. 2.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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