Van Lamoenov izrek

diplomsko delo

Dominika Žugman (Author), Bojan Hvala (Mentor)

Abstract

V diplomskem delu dokažemo van Lamoenov izrek, ki pravi, da središča očrtanih krogov šestih trikotnikov, na katere težiščnice razdelijo dani trikotnik ABC, ležijo na krožnici. Kasneje vpeljemo enačbo stožnice skozi pet točk in omenimo Pascalov izrek na stožnicah. Nato preverimo dejstvo, da šest točk v ravnini vedno leži na krivulji drugega reda v primeru, ko so nosilke nasprotnih stranic šest cikla vzporedne. Kasneje s pomočjo omenjenih rezultatov dokažemo posplošitve van Lamoenovega izreka.

Keywords

Van Lamoenov izrek;težišče;višinska točka;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2012
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[D. Žugman]
UDC:	51(043.2)
COBISS:	19202056
Views:	506
Downloads:	17
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	VAN LAMOEN'S THEOREM
Secondary abstract:	In this graduate thesis we present and prove the van Lamoen's theorem which states that if we split a triangle into a cevasix configuration with three medians the circumcenter of the inner six triangles are concyclic. In continuation we introduce the conic equasion through five points and mention the Pascal theorem on conics. Then we verify the fact that six points on a plane always lie on a conic when the opposite sides of a hexagon are parallel. With the help of the aforementioned results we can later prove the generalizations of the van Lamoen's theorem.
Secondary keywords:	Van Lamoen's Theorem;circumcenter;centroid;orthocenter.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fakulteta za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	48 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	8717506