Kompleksna števila v geometriji

magistrsko delo

Olivija Grafenauer (Author), Uroš Kuzman (Mentor)

Abstract

V magistrski nalogi s pomočjo kompleksnih števil obravnavam nekatere geometrijske izreke. V prvem delu naloge predstavim kompleksno interpretacijo osnovnih geometrijskih pojmov, ki jih nato uporabim pri dokazovanju nekaterih klasičnih geometrijskih izrekov, kot so Cliffordovi izreki, izrek o obstoju krožnice devetih točk, izrek o Simsonovi premici in Simsonov izrek za štirikotnike, Cantorjevi izreki, Feuerbachov izrek, Morleyev izrek. Nalogo zaključim z novejšim rezultatom, ki je bil dokazan šele leta 2001 - kompleksnim Descartesovim izrekom.

Keywords

kompleksna števila;geometrija;kompleksni Descartesov izrek;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[O. Grafenauer]
UDC:	514
COBISS:	18807897
Views:	1346
Downloads:	244
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Complex numbers in geometry
Secondary abstract:	In my masters thesis I consider some geometric theorems with the help of complex numbers. The thesis consists of complex interpretation of some of the basic geometric terms, with the help of which I consider a set of geometric theorems, such as the Clifford theorems, the nine point circle theorem, the Simsons line theorem and its generalization for quadrilaterals, the Cantor theorems, the Feuerbach theorem, the Morley theorem. Finally, I consider a result that has been proven in the year 2001 - the complex Descartes theorem.
Secondary keywords:	complex numbers;geometry;complex Descartes theorem;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages:	IX, 57 str.
ID:	11288764