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Title:
Arbelos, parabelos in f-belos
Authors:
ID
Ternar, Viktorija
(Author)
ID
Hvala, Bojan
(Mentor)
More about this mentor...
Files:
MAG_Ternar_Viktorija_2015.pdf
(1,49 MB)
MD5: B9D5BEB6884A1D438A800D8D25577F7C
Language:
Slovenian
Work type:
Master's thesis/paper
Typology:
2.09 - Master's Thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
Magistrsko delo obravnava arbelos, parabelos in f-belos. Izhodišče predstavlja arbelos, to je lik omejen s tremi paroma dotikajočimi se polkrožnicami, katerih središča so kolinearna. Če polkrožnice nadomestimo z loki latus rectum parabol, dobimo njegov parabolični analog, ki se imenuje parabelos. f-belos pa je lik, ki predstavlja posplošitev tako arbelosa kot tudi parabelosa. V prvem poglavju so navedene definicija in elementarne lastnosti arbelosa. V drugem poglavju se najprej spomnimo osnovnih pojmov, povezanih s parabolo, nato definiramo parabelos in dokažemo analogne lastnosti kot pri arbelosu. V zadnjem poglavju definiramo f-belos, ki za osnovo vzame (skoraj) poljubno funkcijo, zvezno na intervalu [0,1] in odvedljivo na intervalu (0,1). Omejen je namreč s tremi poljubnimi, vendar podobnimi krivuljami, zato njegove lastnosti predstavljajo razširitev in posplošitev lastnosti arbelosa in parabelosa. V tem delu izpeljemo karakterizaciji arbelosa in parabelosa, kar je tudi osrednji rezultat tega magistrskega dela.
Keywords:
arbelos
,
parabelos
,
f-belos
,
latus rectum
,
temenski paralelogram
,
tangentni paralelogram
Place of publishing:
Maribor
Publisher:
[V. Ternar]
Year of publishing:
2015
PID:
20.500.12556/DKUM-47917
UDC:
514.1:(043.2)
COBISS.SI-ID:
21403400
NUK URN:
URN:SI:UM:DK:KJGQVUKY
Publication date in DKUM:
05.06.2015
Views:
2141
Downloads:
176
Metadata:
Categories:
FNM
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Vancouver
:
TERNAR, Viktorija, 2015,
Arbelos, parabelos in f-belos
[online]. Master’s thesis. Maribor : V. Ternar. [Accessed 30 March 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=47917
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Secondary language
Language:
English
Title:
Arbelos, parabelos and f-belos
Abstract:
The Master's thesis presents geometric shapes, named arbelos, parbelos and f-belos. We start with the arbelos, which is a classical geometric shape, bounded by three mutually tangent semicircles with collinear diameters. If we replace the semicircles with latus rectum arcs parables, we arrive to a parabolic analogue called parbelos. The f-belos is a geometric shape representing a generalization of both the arbelos and the parbelos. The first chapter reveals the definition and the basic characteristics of the arbelos. The second chapter presents the concepts connected to the parable. Next we define the parbelos and prove analogies to similar properties of the arbelos. In the last chapter, however, we define the f-belos, which is based on an (almost) arbitrary function f:[0,1]->R, continuous on [0,1] and differentiable on (0,1). The f-belos is bounded by three random, but similar curves; therefore its characteristics represent an expansion and generalization of the arbelos and parbelos features. In this part of the thesis we derive the characterisations of the arbelos and the parbelos, which are seen as the main result of this Master's thesis.
Keywords:
arbelos
,
parbelos
,
f-belos
,
latus rectum
,
cusp-vertices parallelogram
,
tangent parallelogram
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