Ceva, Menelaus, and selftransversality
type: Item
instance of: scholarly article
title: Ceva, Menelaus, and selftransversality
zbMATH Open document ID: 0883.52005
DOI: 10.1023/A:1017930624603
author: Branko Grünbaum
author: G. C. Shephard
published in: Geometriae Dedicata
publication date: 1998-03-03T00:00:00Z
review text: The theorems of Ceva and Menelaus are well-known results in the elementary geometry of triangles. Since the early 19th century they have been generalized to polygons with more sides and in various other directions. The purpose of this paper is to formulate and prove a Ceva-Menelaus-selftransversality theorem. This theorem makes assertions not only about the ratios of lengths of line segments, but also about ratios of areas and volumes of triangles and simplices defined by the vertices of the \(n\)-gon and by transversals of appropriate dimension. A number of examples is given.
Mathematics Subject Classification ID: 52A38
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 1019776
zbMATH Keywords: lengths
zbMATH Keywords: area
zbMATH Keywords: volumes
zbMATH Keywords: \(n-\)acrons (generalizations of \(n-\)gons)
zbMATH Keywords: elementary problems in Euclidean geometries
zbMATH Keywords: Ceva' theorem
zbMATH Keywords: Menelaus' theorem
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
full work available at URL: a:1017930624603
OpenAlex ID: W5131059
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description: scientific article; zbMATH DE number 1019776