The Hajja–Martini inequality in a weak absolute geometry

Davit Harutyunyan, Aram Nazaryan, Victor Pambuccian

Research output: Contribution to journalArticle

Abstract

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
Volume110
Issue number2
DOIs
StatePublished - Aug 1 2019

Fingerprint

Triangle
P-point

Keywords

  • Absolute plane geometry
  • geometric inequalities

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

The Hajja–Martini inequality in a weak absolute geometry. / Harutyunyan, Davit; Nazaryan, Aram; Pambuccian, Victor.

In: Journal of Geometry, Vol. 110, No. 2, 24, 01.08.2019.

Research output: Contribution to journalArticle

Harutyunyan, Davit ; Nazaryan, Aram ; Pambuccian, Victor. / The Hajja–Martini inequality in a weak absolute geometry. In: Journal of Geometry. 2019 ; Vol. 110, No. 2.
@article{c33caf225c6848488b218fae6a3d38a0,
title = "The Hajja–Martini inequality in a weak absolute geometry",
abstract = "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.",
keywords = "Absolute plane geometry, geometric inequalities",
author = "Davit Harutyunyan and Aram Nazaryan and Victor Pambuccian",
year = "2019",
month = "8",
day = "1",
doi = "10.1007/s00022-019-0481-3",
language = "English (US)",
volume = "110",
journal = "Journal of Geometry",
issn = "0047-2468",
publisher = "Birkhauser Verlag Basel",
number = "2",

}

TY - JOUR

T1 - The Hajja–Martini inequality in a weak absolute geometry

AU - Harutyunyan, Davit

AU - Nazaryan, Aram

AU - Pambuccian, Victor

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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.

KW - Absolute plane geometry

KW - geometric inequalities

UR - http://www.scopus.com/inward/record.url?scp=85065638674&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065638674&partnerID=8YFLogxK

U2 - 10.1007/s00022-019-0481-3

DO - 10.1007/s00022-019-0481-3

M3 - Article

AN - SCOPUS:85065638674

VL - 110

JO - Journal of Geometry

JF - Journal of Geometry

SN - 0047-2468

IS - 2

M1 - 24

ER -