The perimeter sixpartite center of a triangle
type: Item
instance of: scholarly article
title: The perimeter sixpartite center of a triangle
zbMATH Open document ID: 1384.51034
author: Allan Berele
author: Stefan Catoiu
published in: Journal of Geometry
publication date: 2017-12-14T00:00:00Z
review text: The three medians of a triangle meet at the center of gravity and divide the triangle into six triangles of equal areas. The center of gravity is the unique area sixpartite point of a triangle. The authors of this article examine by analogy the existence of perimeter sixpartite point of a triangle. The perimeter bisecting points exists and the three corresponding cevian meet at the Nagel point of the triangle. In any triangle \(ABC\) there are three points \(A'\), \(B'\) and \(C'\) trisecting the perimeter such that the cevians \(AA'\), \(BB'\) and \(CC'\) concur at a point, called the trisected perimeter point \((X_{369})\). The perimeter bisecting deltoid of a triangle are used to study properties of three coincident perimeter bisecting lines. The most important result of the article is the following: ``Every triangle has an unique perimeter sixpartite point'' (Theorem 5). This point is non-constructible and it is not a known triangle center listed in the online Encyclopedia of triangle centers.
reviewed by: Sándor N. Kiss
Mathematics Subject Classification ID: 51N20
zbMATH DE Number: 6818616
zbMATH Keywords: perimeter sixpartite center
zbMATH Keywords: sixpartite point
zbMATH Keywords: perimeter bisecting lines
zbMATH Keywords: envelope
zbMATH Keywords: deltoid
zbMATH Keywords: perimeter bisecting deltoid
MaRDI profile type: Publication
full work available at URL: s00022-017-0380-4
OpenAlex ID: W2606911552
cites work: Some Properties of Triangles as Extremal Convex Curves
cites work: Q4325520
DOI: 10.1007/S00022-017-0380-4
description: scientific article; zbMATH DE number 6818616