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Razmerje med obsegom in premerom kroga v ravninskih metrikah : diplomsko delo
Medvešček, Maša (Author), Slapar, Marko (Mentor) More about this mentor... This link opens in a new window, Horvat, Eva (Co-mentor)

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/id/eprint/5377 This link opens in a new window

Abstract
V diplomskem delu se ukvarjamo z razmerjem med obsegom in premerom kroga v ravninskih metrikah. Za začetek definiramo metriko kot funkcijo merjenja razdalj in si ogledamo nekaj posebnih primerov metrik poleg nam že znane evklidske metrike. Predstavimo taksi metriko, maksimum metriko in splošno p-metriko. V nadaljevanju predstavimo načine računanja dolžine loka v vseh prej omenjenih metrikah z metodo aproksimacije in uporabo Lagrangeovega izreka. V glavnem delu diplomskega dela s pomočjo formule za obseg in dolžine loka izračunamo vrednost števila pi v različnih metrikah. Na koncu dela dokažemo tudi, da pi v evklidski metriki res doseže minimalno vrednost.

Language:Slovenian
Keywords:evklidska metrika, taksi metrika, maksimum metrika, p-metrika, dolžina loka, minimalna vrednost števila pi
Work type:Bachelor thesis/paper (mb11)
Tipology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Year:2018
Publisher:[M. Medvešček]
Number of pages:24 str.
UDC:514.757.3(043.2)
COBISS.SI-ID:12148041 Link is opened in a new window
Views:312
Downloads:139
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Secondary language

Language:English
Title:The ratio of circumference of a circle to its diameter in plane metrics
Abstract:
In diploma thesis, we investigate the ratio of circumference and diameter of a circle in the Euclidean plane. Firstly we define a metric as a function for measuring distances and introduce a few special cases of metrics beside the already known Euclidean one. We present the taxicab metric, maximum metric, and p-metric. In the next part we show how to calculate the arc length of a curve in Euclidean space with geodesic approximation method and usage of Lagrange theorem. The main part consists of calculating the value of pi in different metrics using the formula for circumference of a circle and the arc length. In conclusion, we prove that the value of pi is actually minimal in the Euclidean metric.

Keywords:geometry, geometrija

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