The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra

Autor:	Mostafa Hayajneh, Mowaffaq Hajja, Sadi Abu-Saymeh
Rok vydání:	2012
Předmět:	Combinatorics Lemma (mathematics) Calculus Tetrahedron Geometry and Topology Open mouth Mathematics
Zdroj:	Journal of Geometry. 103:1-16
ISSN:	1420-8997 0047-2468
DOI:	10.1007/s00022-012-0116-4
Popis:	Propositions 24 and 25 of Book I of Euclid’s Elements state the fairly obvious fact that if an angle in a triangle is increased (without changing the lengths of its arms), then the length of the opposite side increases. In less technical terms, the wider you open your mouth, the farther apart your lips are. In this paper, we see that this has a very satisfactory analogue for orthocentric (but not for general) tetrahedra.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::de04296ca140ca7997f248a90fb94da9 https://doi.org/10.1007/s00022-012-0116-4 Zobrazit plný text záznamu Full text from SpringerLink