### 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 language | English (US) |
---|---|

Article number | 24 |

Journal | Journal of Geometry |

Volume | 110 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2019 |

### Fingerprint

### Keywords

- Absolute plane geometry
- geometric inequalities

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Geometry*,

*110*(2), [24]. https://doi.org/10.1007/s00022-019-0481-3

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

Research output: Contribution to journal › Article

*Journal of Geometry*, vol. 110, no. 2, 24. https://doi.org/10.1007/s00022-019-0481-3

}

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

VL - 110

JO - Journal of Geometry

JF - Journal of Geometry

SN - 0047-2468

IS - 2

M1 - 24

ER -