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Title:
Kam postaviti oznako večkotnika?
Authors:
ID
Božič, Aljaž
(Author)
ID
Hvala, Bojan
(Mentor)
More about this mentor...
Files:
MAG_Bozic_Aljaz_2018.pdf
(2,60 MB)
MD5: E0F8ECBF4CF3C2A18CDA437C2CEE02D0
PID:
20.500.12556/dkum/c8d41740-7535-45b0-ac66-5bca7450cf57
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 se najprej seznanimo s trilinearnimi in baricentričnimi koordinatami. Nato spoznamo izotomično in izogonalno transformacijo. Po uvodnih pojmih je podrobneje opisan problem, ki ga rešujemo postopoma. Začnemo z najenostavnejšimi liki, katerih geometrijo dokaj dobro poznamo. Pri iskanju točke, ki bi bila primerna za postavitev oznake večkotnika, naletimo na ogromno kandidatov, vendar se izkaže, da jih ima večina določene pomanjkljivosti. Po opisanem postopku iskanja primerne točke in nekaj primerih se zopet vrnemo k trikotniku saj določimo algoritem, ki nas za poljubni večkotnik pripelje do točke, kjer moramo poiskati primerno točko ravno v trikotniku. Tu se srečamo s trikotniku včrtanimi elipsami in najbolj značilne tudi opišemo. Posebej obravnavamo tudi Lemoinovo elipso in Spiekerjevo točko, kar je tudi rešitev našega problema.
Keywords:
vzporedni večkotnik
,
Spiekerjeva točka
,
Lemoinova elipsa
,
trilinearne koordinate
,
baricentrične koordinate
,
včrtana elipsa
,
izotomična transformacija
,
izogonalna transformacija
,
Nagelova točka
,
Gergonnova točka
Place of publishing:
Maribor
Publisher:
[A. Božič]
Year of publishing:
2018
PID:
20.500.12556/DKUM-69620
UDC:
514.12(043.2)
COBISS.SI-ID:
23696904
NUK URN:
URN:SI:UM:DK:Z0SV9T6K
Publication date in DKUM:
09.03.2018
Views:
1475
Downloads:
130
Metadata:
Categories:
FNM
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:
BOŽIČ, Aljaž, 2018,
Kam postaviti oznako večkotnika?
[online]. Master’s thesis. Maribor : A. Božič. [Accessed 13 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=69620
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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:
11.02.2018
Secondary language
Language:
English
Title:
Where should the label for a polygon be placed?
Abstract:
In the following master thesis we first learn about trilinears, barycentrics. Then we describe isotomic and isogonal conjugate. After describing the main problem, we start searching for the most optimal place for placing laber for a polygon. We start with triangle and quadrilateral and we find out, that a lot of possible candidates (points) have some imperfections. According to the procedure described for a suitable point and some examples, we return to the triangle again since we define an algorithm that leads us to conclusion that a point for placing a label for general polygon is a point in triangle which we get as result of algorithm. We consider ellipses inscribed in the triangle and some triangle centres related to these ellipses. At the end we show results related to Lemoine ellipse and Spieker centre, which are closely connected with the final step of the solution to our problem.
Keywords:
the centre of a polygon
,
parallel polygon
,
Spieker centre
,
Lemoine ellipse
,
trilinears
,
barycentrics
,
inscribed ellipse
,
izotomic conjugate
,
isogonal conjugate
,
Nagel point
,
Gergonne point
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