20.500.12556/RUL-168729 Obstoj včrtanega kvadrata v Jordanovih krivuljah magistrsko delo Existence of an inscribed square in Jordan curves Magistrsko delo temelji na teoretičnem pristopu raziskovanja. Osredotoča se na problem včrtanega kvadrata, ki sprašuje po obstoju štirih točk na Jordanovi krivulji, ki tvorijo oglišča kvadrata. To vprašanje je prvi formuliral Otto Toeplitz leta 1911, zato mu pravimo tudi Toeplitzova domneva. Do tega trenutka problem ostaja v splošnem nerešen, kar pa ne velja v primeru dodatnih predpostavk o dani krivulji (kot sta recimo gladkost in konveksnost). V tem magistrskem delu sta predstavljena dva primera problema včrtanega kvadrata ob dveh različnih dodatnih predpostavkah o Jordanovi krivulji, sledi pa obravnava člankov Arnolda Emcha o obstoju včrtanega kvadrata v gladkih konveksnih Jordanovih krivuljah in Richarda P. Jerrarda o obstoju včrtanega kvadrata v realnih analitičnih Jordanovih krivuljah. The master's thesis is based on a theoretical research approach. It focuses on the square peg problem, which asks whether there exist four points on a Jordan curve that form the vertices of a square. This question was first formulated by Otto Toeplitz in 1911, hence it is also known as the Toeplitz conjecture. To this day, the problem remains generally unsolved, although it can be resolved under additional assumptions about the curve (such as smoothness and convexity). In this master's thesis, two instances of the inscribed square problem are presented under two different additional assumptions about the Jordan curve. Following this, we discuss Arnold Emch's article on the existence of an inscribed square in smooth convex Jordan curves and Richard P. Jerrard's article on the existence of an inscribed square in real analytic Jordan curves. Matematika Konveksna geometrija Kvadrat Enostavne krivulje Jordanova krivulja konveksna krivulja problem včrtanega kvadrata realna analitična krivulja Jordan curve convex curve square square peg problem real analytic curve true false false M. Levak Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-04-19 08:30:55 2025-04-19 08:30:57 2025-04-22 09:28:13 0000-00-00 00:00:00 2025 0 Ljubljana 0 Ljubljana 71 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514(043.2) 184447 233422339 39505.pdf 39505.pdf 1 9AA5D937A75F70BA7B69FD4683D00320 1e51bee80533ff17aaf3b6f5e860956b4a155c6a3dc24e473cda1612c631b144 b8f559e7-1ce6-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=209620 Pedagoška fakulteta 0 0 0