diplomsko delo
Anja Kocbek (Author), Bojan Hvala (Mentor)

Abstract

V diplomskem delu obravnavamo posplošeno Gergonnovo točko. V začetnih poglavjih vpeljemo vse potrebne pojme, definiramo Gergonnovo točko in povzamemo nekaj zanimivih povezav z drugimi značilnimi točkami trikotnika. Nato vpeljemo trilinearne in baricentrične koordinate, ki so ključnega pomena za nadaljnje delo. S pomočjo le-teh, in s pomočjo Cevovega izreka, najprej dokažemo, da posplošena Gergonnova točka obstaja, nato pa izračunamo njene koordinate. V nadaljevanju raziskujemo tir gibanja posplošene Gergonnove točke in določimo skrajne točke. Na koncu ugotovimo, da je tir gibanja krivulja, ki je del neke določene hiperbole. To krivuljo tudi grafično predstavimo.

Keywords

matematika;Gergonnova točka;krožnice;koordinate;hiperbola;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Source: Maribor
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [A. Kocbek]
UDC: 51(043.2)
COBISS: 18588168 Link will open in a new window
Views: 2204
Downloads: 190
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Other data

Secondary language: English
Secondary title: GENERALIZED GERGONNE POINT
Secondary abstract: In this graduate thesis we consider the generalized Gergonne point. In the first part of the thesis we get aquainted with Gergonne point. We also summarize some information about Gergonne point and its relation to other triangle centers. Later, we introduce trilinear and barycentric coordinates. We use these coordinates and Ceva's theorem in order to prove that generalized Gergonne point actually exists. Then we also calculate its coordinates. In addition, we investigate the trace of the generalized Gergonne point and define the extreme points. At the end we conclude that our curve is a part of a known hyperbola.
Secondary keywords: Gergonne point;generalized Gergonne point;incircle;trilinear coordinates;barycentric coordinates;hyperbola.;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 50 f.
Keywords (UDC): mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID: 19453
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