na študijskem programu 2. stopnje Matematika
Vanda Štern (Author), Bojan Hvala (Mentor)

Abstract

Grinbergov izrek trdi, da se krožna cevianska konjugacija izraža kot kompozitum, v katerem nastopajo izotomična in izogonalna konjugacija, razteg s središčem v težišču G in koeficientom -1/2 ter njegov inverz. V magistrskem delu bosta predstavljena sintetični dokaz in direkten dokaz s pomočjo trilinearnih koordinat. Obravnavali bomo vse preslikave, predstavili trilinearne koordinate in poiskali enačbe različnih krožnic v trikotniku.

Keywords

magistrska dela;geometrija trikotnika;krožna cevianska konjugacija;izotomična konjugacija;Grinberg;Darij;1988-;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [V. Štern]
UDC: 514.112.3(043.2)
COBISS: 23990275 Link will open in a new window
Views: 505
Downloads: 66
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Other data

Secondary language: English
Secondary title: Grinberg's theorem
Secondary abstract: Grinberg's theorem states that cyclocevian conjugation can be expressed as a composition of transformations, in which occur the following transformations: isotomic conjugate, isogonal conjugate, complement and anticomplement. The master's thesis will present synthetic proof and direct proof using trilinear coordinates. We will consider all the mappings involved, present trilinear coordinates and derive equations of diffrent circles in triangle geometry.
Secondary keywords: master theses;triangle geometry;cyclocevian conjugate;isotomic conjugate;isogonal conjugate;Grinberg;
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: VIII, 49 f.
ID: 11460140
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