Routhov izrek

diplomsko delo

Mihaela Remic (Author), Matija Cencelj (Mentor), Tadej Starčič (Co-mentor)

Abstract

V elementarni geometriji je eden najpomembnejših izrekov o geometriji trikotnikov Cevov izrek. Cevov izrek podaja kriterij, kdaj množica treh Cevovih premic, po ena skozi vsako oglišče in točko nasprotiležne stranice danega trikotnika, tvori šop. Routhov izrek je neke vrste posplošitev Cevovega izreka, saj v primeru, da dane Cevove premice ne tvorijo šopa, poda razmerje ploščin danega trikotnika in trikotnika, ki ga dobimo s presečišči Cevovih premic. V diplomskem delu predstavimo in dokažemo Routhov izrek s pomočjo Menelajevega izreka. V zadnjem delu diplomskega dela pa predstavimo še posplošitev Routhovega izreka za primer, ko imamo šest Cevovih premic, po en par premic skozi vsako oglišče danega trikotnika.

Keywords

trikotnik;Cevov izrek;ploščina trikotnika;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Remic]
UDC:	514(043.2)
COBISS:	11120457
Views:	899
Downloads:	171
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Routh's theorem
Secondary abstract:	The Ceva's theorem is one of the most important theorems in elementary geometry. This theorem provides criteria under which a set of three Ceva's line segments, one through each vertex and a point of opposite lying side of the given triangle are concurrent. The Routh's theorem is a kind of generalization of the Ceva's theorem. When the given Ceva's lines are not concurrent, the Routh's theorem gives the ratio between the areas of the given triangle and the triangle, which we get with the intersection of the Ceva's lines. In this work we present and prove the Routh's theorem with the help of the Menelauses' theorem. In the last part of this work we present the generalization of the Routh's theorem to the case when six Ceva's line segments are given, one pair through each vertex of the given triangle.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Matematika in fizika
Pages:	VIII, [60] str.
ID:	9165363