On polygons inscribed in other polygons
type: Item
instance of: scholarly article
zbMATH Open document ID: 1257.51008
author: Paris Pamfilos
publication date: 2012-09-25T00:00:00Z
full work available at URL: jgg15011.htm
Mathematics Subject Classification ID: 51M04
Mathematics Subject Classification ID: 51N10
zbMATH DE Number: 6086378
zbMATH Keywords: Thomsen's figure
zbMATH Keywords: Ceva's theorem
zbMATH Keywords: inscribed polygons
MaRDI profile type: Publication
title: On polygons inscribed in other polygons
published in: Journal for Geometry and Graphics
review text: Assume we are given a polygon \(p=P_0\dots P_{n-1}\), where \(P_i\) denotes the vertices of \(p\). We are also given a set of unit plane vectors \(\{v_1,\dots, v_{n-1}\}\). Denote by \(\alpha_i\) the straight line defined by the vertices \(P_i\) and \(P_{i+1}\).NEWLINENEWLINEStarting with a point \(X_0\in\alpha_0\) we construct a polygon \(X_0\dots X_{n-1}\) satisfying the following conditions:NEWLINENEWLINE(i) \(X_i\in\alpha_i\) andNEWLINENEWLINE(ii) the line \(X_iX_{i+1}\) is parallel to \(v_i\).NEWLINENEWLINEThe paper is concerned about the existence of closed polygons (i.e., such that \(X_0=X_{n-1}\)) constructed under the previous conditions. In the triangular case a close relation to Ceva's theorem is found.
reviewed by: Antonio M. Oller Marcén
description: scientific article; zbMATH DE number 6086378