20.500.12556/DKUM-47917 Arbelos, parabelos in f-belos Arbelos, parabelos and f-belos Magistrsko delo obravnava arbelos, parabelos in f-belos. Izhodišče predstavlja arbelos, to je lik omejen s tremi paroma dotikajočimi se polkrožnicami, katerih središča so kolinearna. Če polkrožnice nadomestimo z loki latus rectum parabol, dobimo njegov parabolični analog, ki se imenuje parabelos. f-belos pa je lik, ki predstavlja posplošitev tako arbelosa kot tudi parabelosa. V prvem poglavju so navedene definicija in elementarne lastnosti arbelosa. V drugem poglavju se najprej spomnimo osnovnih pojmov, povezanih s parabolo, nato definiramo parabelos in dokažemo analogne lastnosti kot pri arbelosu. V zadnjem poglavju definiramo f-belos, ki za osnovo vzame (skoraj) poljubno funkcijo, zvezno na intervalu [0,1] in odvedljivo na intervalu (0,1). Omejen je namreč s tremi poljubnimi, vendar podobnimi krivuljami, zato njegove lastnosti predstavljajo razširitev in posplošitev lastnosti arbelosa in parabelosa. V tem delu izpeljemo karakterizaciji arbelosa in parabelosa, kar je tudi osrednji rezultat tega magistrskega dela. The Master's thesis presents geometric shapes, named arbelos, parbelos and f-belos. We start with the arbelos, which is a classical geometric shape, bounded by three mutually tangent semicircles with collinear diameters. If we replace the semicircles with latus rectum arcs parables, we arrive to a parabolic analogue called parbelos. The f-belos is a geometric shape representing a generalization of both the arbelos and the parbelos. The first chapter reveals the definition and the basic characteristics of the arbelos. The second chapter presents the concepts connected to the parable. Next we define the parbelos and prove analogies to similar properties of the arbelos. In the last chapter, however, we define the f-belos, which is based on an (almost) arbitrary function f:[0,1]->R, continuous on [0,1] and differentiable on (0,1). The f-belos is bounded by three random, but similar curves; therefore its characteristics represent an expansion and generalization of the arbelos and parbelos features. In this part of the thesis we derive the characterisations of the arbelos and the parbelos, which are seen as the main result of this Master's thesis. arbelos parabelos f-belos latus rectum temenski paralelogram tangentni paralelogram arbelos parbelos f-belos latus rectum cusp-vertices parallelogram tangent parallelogram true true false [V. Ternar] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2015-04-24 15:58:22 2015-06-05 13:37:47 2022-05-23 03:06:59 2021-05-08 03:21:12 2015 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514.1:(043.2) 21403400 URN:SI:UM:DK:KJGQVUKY MAG_Ternar_Viktorija_2015.pdf MAG_Ternar_Viktorija_2015.pdf 1 B9D5BEB6884A1D438A800D8D25577F7C 083cf7cda178e02b1dca3b9e6d2cefe506a86a4b939e42592eb27db4deea523c 9e2f965b-7c0b-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=71478 Fakulteta za naravoslovje in matematiko 0 0 0