20.500.12556/RUL-169367 Origami konstrukcije in reševanje problemov s prepogibanjem papirja magistrsko delo Origami constructions and problem solving by paper-folding Prepogibanje papirja je v zadnjih petdesetih letih dobilo veliko vrednost v znanosti. Z ravnimi in enkratnimi prepogibi ter z njihovimi presečišči so določene premice in točke v modelu evklidske ravnine, vendar origamija ne povezujemo le z običajno evklidsko geometrijo. Z njim rešujemo različne probleme, ki izhajajo tudi iz področja algebre, teorije števil, projektivne geometrije, analize in še mnogo drugih. V nalogi bomo definirali množico origami števil in konstrukcije, ki jih lahko opravljamo s prepogibanjem papirja. Pogledali si bomo, kako lahko z origamijem rešujemo predvsem probleme, ki jih z evklidskim orodjem ne moremo, pri čemer je v ospredju vprašanje konstrukcije pravilnega sedemkotnika, trisekcije kota in konstrukcije razdalje $\sqrt[3]{2}$. Spoznali bomo Hagove izreke, prepogibali tangente na stožnice, reševali enačbe tretje in četrte stopnje, na koncu pa še iz več zornih kotov spoznali optični Alhazenov problem in origami konstrukcijo njegove rešitve s pomočjo dualnih stožnic. Paper folding has gained significant value in science over the last fifty years. With straight and single folds and their intersections, lines and points in the model of the Euclidean plane are defined, but origami is not only associated with conventional Euclidean geometry. It helps us solve various problems that stem also from areas like algebra, number theory, projective geometry, analysis, and many others. In this paper, we will define the set of origami numbers and constructions that can be performed through paper folding. We will examine how origami can help solve problems where Euclidean tools are powerless, focusing particularly on the question of construction of regular heptagon, angle trisection and the construction of the distance $\sqrt[3]{2}$. We will get to know Haga's theorems, fold tangents to conics, solve cubic and quartic equations, and finally, from various perspectives, learn about Alhazen's optical problem and the origami construction of its solution with help of dual conics. Prepogibanje papirja origami operacije Belochin pregib origami konstrukcije origami števila Hagovi izreki trisekcija kota podvojitev kocke prepogibanje tangent na stožnice Lillova metoda reševanje enačb dualne stožnice Alhazenov problem. Paper folding origami operations Beloch's fold origami constructions origami numbers Haga's theorems angle trisection doubling the cube folding tangents to conics Lill's method equation solving dual conics Alhazen's problem. true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-05-25 08:15:05 2025-05-25 08:15:12 2025-05-26 10:27:20 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514 150237 237012995 16759.pdf 16759.pdf 1 D62C4F5E4B4C80E92295C6CD8A023E7C 16d0a603b5280163ba55771d347ebb2433400ce9a591773e5e4a31e35d9f946c 54328529-392e-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=210668 Fakulteta za matematiko in fiziko 0 0 0