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Dolžina loka v ravninski p-metriki
Tisovec, Anja (Author), Slapar, Marko (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/3844/ This link opens in a new window

Abstract
V diplomski nalogi se ukvarjamo z računanjem dolžine loka v ravninski p-metriki. Najprej definiramo metriko kot funkcijo merjenja razdalje in si ogledamo nekaj konkretnih osnovnih primerov metrik ter nadaljujemo s predstavitvijo nekaj splošno znanih izračunov razdalje v evklidskem prostoru. Spoznamo taksi metriko, maksimum metriko in bolj splošno p-metriko. Vsako od navedenih metrik utemeljimo s pomočjo štirih aksiomov metrike in obravnavamo nekaj osnovnih lastnosti p-metrike. V drugem in hkrati glavnem delu diplomskega dela predstavimo načine računanja dolžine loka v prej navedenih metrikah v ravnini z metodo aproksimacije.

Language:Slovenian
Keywords:evklidska metrika
Work type:Bachelor thesis/paper (mb11)
Tipology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Year:2016
COBISS.SI-ID:11205193 This link opens in a new window
Views:763
Downloads:165
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Secondary language

Language:English
Title:Arc length in planar p-metric
Abstract:
In this diploma thesis, we show how to calculate the ark length of a plane curve in the planar p-metric. We first give some basic concrete examples of metrics and then continue with presenting the standard distance functions in Euclidian spaces. We get familiar with the taxicab metric, maximum metric and the more general p-metric. We show that each of them satisfies the four axioms of metric functions and present some basic properties of p-metrics. In the second and main part of our diploma thesis, we show how to calculate the arc length of a curve in all these different metrics in the plane, using the geodesic approximation method.

Keywords:Euclidian metric

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