20.500.12556/DKUM-17894 VAN AUBELOV IZREK VAN AUBELS THEOREM V diplomskem delu sta v prvem delu predstavljena Napoleonov in Thebaultov izrek, ki sta z Van Aubelovim izrekom tesno povezana. Van Aubelov izrek temelji na konstrukciji kvadratov nad stranicami poljubnega štirikotnika. Kot rezultat dobimo, da sta daljici, ki povezujeta središči nasprotnih kvadratov, enako dolgi in pravokotni. Najprej izrek dokažemo na klasičen geometrijski način, nato še s pomočjo kompleksnih števil, izometrij ravnine in vektorjev. Ker nam Van Aubelov izrek omogoča veliko posplošitev, ki nam ponovno dajo zanimive rezultate, se v zadnjem delu diplomskega dela srečamo še s predstavitvijo le-teh. Two theorems are presented in the first part of the thesis, Napoleon's and Thebault's. Both of them are strongly connected to Van Aubel's theorem. Van Aubel's theorem is based on the construction of squares which are erected externally on the sides of the quadrilateral. The result is two congruent and perpendicular segment lines, which connect the midpoints of the opposite squares. Initially the theorem is proven by using a classical geometric method and later on by using complex numbers, transformations and vectors. Since the Van Aubel's theorem enables many generalisations which lead to new interesting results the last part of the thesis is devoted to those. Van Aubelov izrek štirikotnik kvadrat pravokotnost kompleksna števila vektorji izometrije ravnine. Van Aubel's theorem quadrilateral square perpendicular complex numbers vectors transformations. true true false [R. Pučko] Slovenski jezik Angleški jezik Diplomsko delo 2011-03-28 20:50:30 2011-04-22 12:25:50 2022-04-13 10:15:00 2023-12-22 03:35:09 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18298632 URN:SI:UM:DK:AUKMK5RN UNI_Pucko_Renata_2011.pdf UNI_Pucko_Renata_2011.pdf 1 0C5159F79236034C0728A73B4381D5D4 b61144c9b340db06303b11c73e3d75ad6da50dcc48ad376e2c0a2de4ba43d528 ffdcb3fb-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/6b901385-b0a3-410b-b059-d62e86e12caf https://dk.um.si/Dokument.php?lang=slv&id=21108 Fakulteta za naravoslovje in matematiko 0 0 0