20.500.12556/DKUM-48401 Posplošena Lucasova konfiguracija Generalized Lucas' configuration V diplomskem delu bomo predstavili konfiguracijo treh trikotniku ABC včrtanih enakostraničnih trikotnikov A_1 A_2 A_3, B_1 B_2 B_3, in C_1 C_2 C_3, od katerih ima vsak eno stranico vzporedno eni od stranic trikotnika ABC. V zvezi s to konfiguracijo bomo dokazali nekaj lastnosti in zanimivosti kot so kolinearnost njihovih težišč, kolinearnost po treh trojic iz množice (devetih) razpolovišč stranic teh trikotnikov, koncikličnost določenih četveric iz množice (devetih) oglišč teh trikotnikov in podobno. Pri delu bomo pretežno uporabljali kartezične koordinate. In this paper we will introduce a configuration of three inscribed equilateral triangles A_1 A_2 A_3, B_1 B_2 B_3, in C_1 C_2 C_3 in a triangle ABC, in which every inscribed triangle has one side parallel to one of the sides of the triangle ABC. Regarding this configuration we will prove some of the characteristics and interesting facts. We will prove collinearity of their centers, we will also show that the mid-points of the sides of the inscribed triangles are collinear three by three, we will find that four by four vertices of the equilateral triangles are concyclic and many other similar facts. In this work we will mainly use Cartesian coordinates. Lucasova konfiguracija Lucasove krožnice konfiguracija včrtanih enakostraničnih trikotnikov Fermatova točka tetivni štirikotnik kolinearnost koncikličnost Lucas' configuration Lucas' circles configuration of inscribed equilateral triangles Fermat point cyclic quadrilateral collinearity concyclic points true true false [D. Fazlič] Slovenski jezik Angleški jezik Diplomsko delo 2015-06-16 16:25:59 2015-10-13 15:54:57 2022-05-25 03:07:03 2024-01-03 03:21:41 2015 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514.112.3(043.2) 21545992 URN:SI:UM:DK:UKCQUMT3 UN_Fazlic_Dinka_2015.pdf UN_Fazlic_Dinka_2015.pdf 1 50D64095C201B4C1D4607EDB2BD82361 2b84810db8719f953b5bd0cbfef02f1a1c2fac07b60da4c61a31323e536b7316 af91a563-7c0b-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=72640 Fakulteta za naravoslovje in matematiko 0 0 0