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Title:Grinbergov izrek
Authors:ID Štern, Vanda (Author)
ID Hvala, Bojan (Mentor) More about this mentor... New window
Files:.pdf MAG_Stern_Vanda_2020.pdf (6,81 MB)
MD5: B645683AEBE463C60ACB61AE9553BF01
PID: 20.500.12556/dkum/54d87565-e2cc-40ee-8fa8-196198d656e1
 
Language:Slovenian
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
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:geometrija trikotnika, krožna cevianska konjugacija, izotomična konjugacija, izogonalna konjugacija, Grinberg
Place of publishing:Maribor
Publisher:[V. Štern]
Year of publishing:2020
PID:20.500.12556/DKUM-75974 New window
UDC:514.112.3(043.2)
COBISS.SI-ID:23990275 New window
NUK URN:URN:SI:UM:DK:59EPRSUS
Publication date in DKUM:30.07.2020
Views:1436
Downloads:104
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:25.03.2020

Secondary language

Language:English
Title:Grinberg's theorem
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.
Keywords:triangle geometry, cyclocevian conjugate, isotomic conjugate, isogonal conjugate, Grinberg


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