20.500.12556/RUL-83441 Pravilni ikozaeder Regular icosahedron V diplomskem delu so zbrane lastnosti pravilnega ikozaedra, ki študentom matematike približajo snov, hkrati pa lahko učitelji matematike pripravijo naloge za nadarjene učence v osnovni ali srednji šoli. V začetnem delu so opisane osnovne lastnosti poliedrov, ki so značilne tako za ikozaeder kot za ostale pravilne poliedre (tetraeder, kocka, dodekaeder, oktaeder). Dokazali smo, da obstaja le pet pravilnih ali platonskih teles in preverili, da zanje velja Eulerjeva poliedrska formula. Nadalje smo se osredotočili le na izbran polieder. Za izračun prostornine smo potrebovali zlato število, ki je pozitivna rešitev Fibonaccijeve enačbe, zato smo le-to izpeljali iz številčnega zaporedja. V zadnjem delu smo ikozaedru priredili graf v ravnini in se posvetili Hamiltonovemu Potovanju okoli sveta oziroma Ikozaedrski igri ter raziskali simetrije ikozaedra. Here are collected properties of regular icosahedron which are useful for students of mathematics or mathematics teachers who can prepare exercises for talented students in elementary or middle school. The initial section describes the basic properties of regular polyhedra: tetrahedron, cube, dodecahedron, octahedron and of course icosahedron. We have proven that there are only five regular or platonic solids and have verified Euler's polyhedron formula for them. Then we focused on selected polyhedron. To calculate the volume we need the golden number which is a positive solution of the Fibonacci equation. In the last part we have made planar graph for icosahedron and have told something about Hamilton's trip around the world (Icosian game) and explore symmetry of icosahedron. pravilni poliedri regular polyhedra true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2016-06-14 03:03:56 2016-08-24 16:12:59 2025-04-17 04:52:27 0000-00-00 00:00:00 2016 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 11039561 Pravilni_ikozaeder_Mihelak.pdf Pravilni_ikozaeder_Mihelak.pdf 1 EE26BA164900C95DDEBAB5EA6173B7F7 8582c01b9d0aad86bad48ee668b3d110da29345e42e6f1b567c92ddc46e0792d 1eb7c562-1aab-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=204557 Pedagoška fakulteta 0 0 0