20.500.12556/RUL-150631 Računanje prostornine konveksnih poliedrov magistrsko delo Volume Calculation of Convex Polyhedra Magistrsko delo temelji na teoretičnem pristopu raziskovanja. V delu raziskujemo različne načine računanja prostornine politopov, predvsem se osredotočimo na dimenziji d = 2 in d = 3. Najpogosteje računamo prostornino s pomočjo same definicije prostornine, to je z ustreznim integralom vzdolž danega politopa. Tak način je zamuden in dolgotrajen, zato se v magistrskem delu osredotočimo na izračun prostornine poliedrov s pomočjo treh pomembnih izrekov in sicer Greenove formule, Stokesovega izreka in Gaussovega divergenčnega izreka. Poseben način računanja prostornine politopov je tudi uporaba triangulacije. Za uporabo triangulacijskih metod potrebujemo obrazec, s katerim izračunamo prostornino simpleksov, ki to triangulacijo sestavljajo. Ta obrazec v delu izpeljemo in razložimo dve metodi ra- čunanja prostornine z uporabo triangulacije. Na koncu naredimo povzetek vseh uporabljenih metod. V zadnjem poglavju se dotaknemo še računanja prostornine v osnovnih in srednjih šolah. Povemo, katere metode se pri tem uporablja, in komentiramo, ali je smiselno narediti z učenci izpeljavo nekaterih obrazcev za računanje prostornine geometrijskih teles. The master's thesis is based on a theoretical research approach. In this work, we investigate different ways of calculating the volume of polytopes, mainly focusing on the dimensions d = 2 and d = 3. Most often, we calculate the volume by definition, that is, by evaluating the corresponding integral along the given polytope. Such computation may be quite long and complicated. Therefore, in the master's thesis, we focus on the calculation of the volume of polyhedra with the help of three important theorems: Green's formula, Stokes' theorem and Gauss's divergence theorem. A special method of calculating the volume of a polytope is the use of triangulation. To use triangulation methods, we need a formula for the volume of a simplex. We include the derivation of this formula and explain two methods of computing the volume of polyhedra using triangulation. At the end of the thesis, we summarize all the methods which were used. In the last chapter, we review how the volume of polytopes is taught in the primary and secondary school education. We discuss whether the methods of volume computation described in this thesis might be used by teachers in the classroom. politop polieder mnogokotnik prostornina poliedra triangulacija polytope polyhedron polygon volume of a polyhedron triangulation true false false T. Rupnik Slovenski jezik Angleški jezik Magistrsko delo/naloga 2023-09-21 08:30:20 2023-09-21 08:30:24 2023-09-22 13:45:03 0000-00-00 00:00:00 2023 0 Ljubljana 0 Ljubljana 55 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.142.3(043.2) 154882 20.500.12556/RUL-150631 165436163 26512.pdf 26512.pdf 1 754B32FA7A3B6904107C65F2E6E40AB8 b03a65e290d3df9ef35355b6e2c1ba5b2caa54b6de8850f0bc30b18bdf9f7124 57d3d144-5848-11ee-82e5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=175262 Pedagoška fakulteta 0 0 0