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Title:Bočni trikotniki in prijateljske značilne točke trikotnika : na študijskem programu 2. stopnje Izbraževalna matematika
Authors:ID Zobovič, Igor (Author)
ID Hvala, Bojan (Mentor) More about this mentor... New window
Files:.pdf MAG_Zobovic_Igor_2025.pdf (887,35 KB)
MD5: D67F2484301109DBE3AD38803BA5A763
 
Language:Slovenian
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V magistrskem delu najprej predstavimo Vectenovo konfiguracijo trikotnika in omenimo njene osnovne lastnosti. Geometrijske elemente Vectenove konfiguracije ponazorimo tudi z uporabo kompleksnih števil in trilinearnih koordinat. Nato definiramo imitativne in imitatorske točke trikotnika. Opišemo množico vseh imitativnih točk trikotnika in množico vseh njihovih imitatorjev. Določimo imitatorje nekaterih imitativnih značilnih točk trikotnika. V tretjem poglavju definiramo prijateljske značilne točke trikotnika in opišemo lastnosti relacije prijateljstva. Določimo prijatelje nekaterih prijateljskih značilnih točk trikotnika, med drugim tudi vseh Kiepertovih perspektorjev s Kiepertove hiperbole trikotnika. V zaključku diskutiramo o bistvenih razlikah med konceptoma imitatorstva in prijateljstva značilnih točk trikotnika.
Keywords:Vectenova konfiguracija, značilne točke trikotnika, Thomsonova in Darbouxjeva kubična krivulja trikotnika, imitativne točke trikotnika, imitatorji, Kiepertovi perspektorji, prijateljske značilne točke trikotnika.
Place of publishing:Maribor
Place of performance:Maribor
Publisher:[I. Zobovič]
Year of publishing:2025
Number of pages:VIII, 54 f.
PID:20.500.12556/DKUM-91563 New window
UDC:514.112.3(043.2)
COBISS.SI-ID:229701379 New window
Publication date in DKUM:20.03.2025
Views:0
Downloads:5
Metadata:XML DC-XML DC-RDF
Categories:FNM
:
ZOBOVIČ, Igor, 2025, Bočni trikotniki in prijateljske značilne točke trikotnika : na študijskem programu 2. stopnje Izbraževalna matematika [online]. Master’s thesis. Maribor : I. Zobovič. [Accessed 4 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=91563
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Licences

License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:15.01.2025

Secondary language

Language:English
Title:Flank triangles and friendship among triangle centres : magistrsko delo
Abstract:In the thesis we first introduce the Vecten configuration of a triangle and we observe its basic properties. We illustrate the geometric elements of the Vecten configuration with the use of complex numbers and trilinear coordinates. We then define imitative triangle points and their imitators. We describe the set of all imitative triangle points and the set of their imitators. We determine the imitators of some imitative triangle points. In the third section we define friendship among triangle centers and describe the relation's properties. We determine the friendships of some triangle centers including the Kiepert perspectors from the Kiepert hyperbola. At the end we discuss the main differences between the concepts of imitation and friendship among triangle centers.
Keywords:Vecten configuration, triangle centers, Thomson and Darboux cubic curve, imitative triangle points, imitators, Kiepert perspectors, friendship among triangle centers.


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