Obstoj včrtanega pravokotnika v Jordanovih krivuljah : delo diplomskega seminarja

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.

Language: Slovenian Jordanove krivulje, realna projektivna ravnina, pravokotniki, kvocientni prostori Bachelor thesis/paper FMF - Faculty of Mathematics and Physics 2021 20.500.12556/RUL-131033 515.1 77661955 22.09.2021 532 40 Copy citation

## Secondary language

Language: English Existence of inscribed rectangle in Jordan curves 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. Jordan curves, real projective plane, rectangles, quotient spaces

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