Posplošena Lucasova konfiguracija

diplomsko delo

Dinka Fazlić (Author), Bojan Hvala (Mentor)

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

diplomska dela;Lucasova konfiguracija;Lucasove krožnice;konfiguracija včrtanih enakostraničnih trikotnikov;Fermatova točka;tetivni štirikotnik;kolinearnost;koncikličnost;

Data

Language:	Slovenian
Year of publishing:	2015
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[D. Fazlič]
UDC:	514.112.3(043.2)
COBISS:	21545992
Views:	900
Downloads:	79
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Generalized Lucas' configuration
Secondary 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.
Secondary keywords:	theses;Lucas configuration;Lucas circle;configuration inscribed equilateral triangles;Fermat point;cyclic quadrilateral;collinearity;concyclicality;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	59 str.
ID:	8760911