The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra
type: Item
instance of: scholarly article
title: The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra
zbMATH Open document ID: 1261.51015
author: Sadi Abu-Saymeh
author: Mowaffaq Hajja
author: M. Hayajneh
published in: Journal of Geometry
publication date: 2013-01-03T00:00:00Z
review text: It is quite evident, and Euclid proved it in Proposition 24, Book I of his Elements, that if an angle of a triangle is increased without changing the length of its arms then the opposite side also increases. In this paper it is shown that an analogue is still true in orthocentric tetrahedra (those with concurrent altitudes) but it is no longer true for general tetrahedra.
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 6121642
zbMATH Keywords: content of a solid angle
zbMATH Keywords: open mouth theorem
zbMATH Keywords: orthocentric tetrahedron
zbMATH Keywords: polar sine
zbMATH Keywords: sine of a solid angle
zbMATH Keywords: solid angle
zbMATH Keywords: trihedral angle
reviewed by: Antonio M. Oller Marcén
MaRDI profile type: Publication
full work available at URL: s00022-012-0116-4
OpenAlex ID: W2006077920
Wikidata QID: Q61534690
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DOI: 10.1007/S00022-012-0116-4
description: scientific article; zbMATH DE number 6121642