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Računanje prostornine konveksnih poliedrov [Elektronski vir] = Volume calculation of convex polyhedra : magistrsko deloRupnik, TerezijaMagistrsko 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.Type of material - master's thesis ; adult, seriousPublication and manufacture - 2023 ; Ljubljana : [T. Rupnik]Language - slovenianCOBISS.SI-ID - 165436163
Author
Rupnik, Terezija
Other authors
Horvat, Eva, 1982-
Topics
Matematika |
Univerzitetna in visokošolska dela |
politop |
polieder |
mnogokotnik |
prostornina poliedra |
triangulacija |
polytope |
polyhedron |
polygon |
volume of a polyhedron |
triangulation
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Rupnik, Terezija | |
Horvat, Eva, 1982- | 29018 |
Source: Personal bibliographies
and: SICRIS
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