Möbiusova ravnina

delo diplomskega seminarja

Primož Bogner (Author), Aleš Vavpetič (Mentor)

Abstract

Namen diplomske naloge je opisati in predstaviti nekatere lastnosti Möbiusovih ravnin. Obravnavo začnemo z idejno razlago Möbiusove ravnine preko Evklidske, uvrstitev v širši razred krožnih ravnin in povezavo z afinimi ravninami. Sledila bo sistematična konstrukcija Möbiusovih ravnin nad poljubno izbranimi polji in izrek, ki takšne kategorizira. Prostorski model nas bo pripeljal do širšega razreda ravnin, ki jih definiramo preko ravninskih presekov ovoidov. Delo zaključimo s podrobnejšo obravnavo značilne preslikave zrcaljenja čez krožnico, podamo nekaj geometrijskih konstrukcij in mero za razdaljo med krožnicami.

Keywords

Möbiusova ravnina;inverzna ravnina;zrcaljenje čez krožnico;Miquelov izrek;inverzna razdalja;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[P. Bogner]
UDC:	514
COBISS:	208200451
Views:	52
Downloads:	1053
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Möbius Plane
Secondary abstract:	The aim of the work is to present construction and some characteristics of Möbius planes. We begin with introducing their concept through the Euclidean plane, their classification into a wider class of circle planes and their connection with affine planes. Continuing with generalised construction over any chosen field and a geometric theorem, that characterizes said contruction, will lead to a space model of Möbius planes. With it, an even wider class of examples will be given as plane sections of ovoids. Final chapter deals with a characteristic mapping circle inversion and its properties, some geometric constructions and a metric for measuring distance between circles.
Secondary keywords:	Möbius plane;inversive plane;circle inversion;theorem of Miquel;inversive distance;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	35 str.
ID:	25059922