Obstoj včrtanega pravokotnika v Jordanovih krivuljah

delo diplomskega seminarja

Jon Pustavrh-Mičović (Author), Aleš Vavpetič (Mentor)

Abstract

Problem včrtanega kvadrata sprašuje po obstoju štirih točk na Jordanovi krivulji, ki tvorijo oglišča kvadrata. Problem je danes še vedno odprt, vendar pa je problem obstoja včrtanega pravokotnika rešen z elementarno topologijo. Obravnava problema včrtanega pravokotnika in teorija, ki jo potrebujemo za rešitev, sta osrednji temi diplomskega dela. Na začetku rešimo posebna primera problema včrtanega kvadrata, potem pa predstavimo kvocientne prostore in se natančneje posvetimo Jordanovim krivuljam.

Keywords

matematika;Jordanove krivulje;realna projektivna ravnina;pravokotniki;kvocientni prostori;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[J. Pustavrh-Mičović]
UDC:	515.1
COBISS:	77661955
Views:	870
Downloads:	58
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Existence of inscribed rectangle in Jordan curves
Secondary abstract:	The inscribed square problem asks for the existence of four points on the Jordan curve that form vertices of a square. Even though that problem remains open, the inscribed rectangle problem has been solved using elementary topology. The analysis of the inscribed rectangle problem and the theory we need to solve it are the central themes of this thesis. At the beginning, we solve two special examples of the inscribed rectangle problem, then we present the quotient spaces and pay more attention to the Jordan curves. In the end, we combine the acquired knowledge into a solution to the inscribed rectangle problem.
Secondary keywords:	mathematics;Jordan curves;real projective plane;rectangles;quotient spaces;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	28 str.
ID:	13505874