Van Aubelov izrek

diplomsko delo

Renata Pučko (Author), Bojan Hvala (Mentor)

Abstract

V diplomskem delu sta v prvem delu predstavljena Napoleonov in Thebaultov izrek, ki sta z Van Aubelovim izrekom tesno povezana. Van Aubelov izrek temelji na konstrukciji kvadratov nad stranicami poljubnega štirikotnika. Kot rezultat dobimo, da sta daljici, ki povezujeta središči nasprotnih kvadratov, enako dolgi in pravokotni. Najprej izrek dokažemo na klasičen geometrijski način, nato še s pomočjo kompleksnih števil, izometrij ravnine in vektorjev. Ker nam Van Aubelov izrek omogoča veliko posplošitev, ki nam ponovno dajo zanimive rezultate, se v zadnjem delu diplomskega dela srečamo še s predstavitvijo le-teh.

Keywords

matematika;Van Aubelov izrek;štirikotnik;kvadrat;pravokotnost;kompleksna števila;vektorji;izometrije ravnine;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[R. Pučko]
UDC:	51(043.2)
COBISS:	18298632
Views:	2486
Downloads:	139
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	VAN AUBELS THEOREM
Secondary abstract:	Two theorems are presented in the first part of the thesis, Napoleon's and Thebault's. Both of them are strongly connected to Van Aubel's theorem. Van Aubel's theorem is based on the construction of squares which are erected externally on the sides of the quadrilateral. The result is two congruent and perpendicular segment lines, which connect the midpoints of the opposite squares. Initially the theorem is proven by using a classical geometric method and later on by using complex numbers, transformations and vectors. Since the Van Aubel's theorem enables many generalisations which lead to new interesting results the last part of the thesis is devoted to those.
Secondary keywords:	Van Aubel's theorem;quadrilateral;square;perpendicular;complex numbers;vectors;transformations.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	51 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19213