The Hajja–Martini inequality in a weak absolute geometry

Davit Harutyunyan, Aram Nazaryan, Victor Pambuccian

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Solving a problem left open in Hajja and Martini (Mitt. Math. Ges. Hamburg 33:135–159, 2013), we prove, inside a weak plane absolute geometry, that, for every point P in the plane of a triangle ABC there exists a point Q inside or on the sides of ABC which satisfies: AQ≤AP,BQ≤BP,CQ≤CP.If P lies outside of the triangle ABC, then Q can be chosen to both lie inside the triangle ABC and such that the inequalities in (1) are strict. We will also provide an algorithm to construct such a point Q.

Original languageEnglish (US)
Article number24
JournalJournal of Geometry
Issue number2
StatePublished - Aug 1 2019


  • Absolute plane geometry
  • geometric inequalities

ASJC Scopus subject areas

  • Geometry and Topology


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