20.500.12556/RUL-131033 Obstoj včrtanega pravokotnika v Jordanovih krivuljah delo diplomskega seminarja Existence of inscribed rectangle in Jordan curves 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. 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. Jordanove krivulje realna projektivna ravnina pravokotniki kvocientni prostori Jordan curves real projective plane rectangles quotient spaces true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2021-09-22 08:15:05 2021-09-22 08:15:06 2024-05-29 13:12:15 0000-00-00 00:00:00 2021 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.1 120622 77661955 3715.pdf 3715.pdf 1 7EB4432CB5448C460B62D64BFFCD26AD 7ecb52eb5f5d47bcefd6132a379695319d818d4c44d331edf9ab0a5d9ba78eed 292dc1ec-1b6c-11ec-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=148264 Fakulteta za matematiko in fiziko 0 0 0