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 |
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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 journal › Article
}
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 -