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Title:Posplošena Lucasova konfiguracija
Authors:ID Fazlić, Dinka (Author)
ID Hvala, Bojan (Mentor) More about this mentor... New window
Files:.pdf UN_Fazlic_Dinka_2015.pdf (1,16 MB)
MD5: 50D64095C201B4C1D4607EDB2BD82361
 
Language:Slovenian
Work type:Undergraduate thesis
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract: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.
Keywords:Lucasova konfiguracija, Lucasove krožnice, konfiguracija včrtanih enakostraničnih trikotnikov, Fermatova točka, tetivni štirikotnik, kolinearnost, koncikličnost
Place of publishing:Maribor
Publisher:[D. Fazlič]
Year of publishing:2015
PID:20.500.12556/DKUM-48401 New window
UDC:514.112.3(043.2)
COBISS.SI-ID:21545992 New window
NUK URN:URN:SI:UM:DK:UKCQUMT3
Publication date in DKUM:13.10.2015
Views:1579
Downloads:150
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:Generalized Lucas' configuration
Abstract: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.
Keywords:Lucas' configuration, Lucas' circles, configuration of inscribed equilateral triangles, Fermat point, cyclic quadrilateral, collinearity, concyclic points


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