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The ratio of circumference of a circle to its diameter in plane metrics

Maša Medvešček (2018) The ratio of circumference of a circle to its diameter in plane metrics. Diploma thesis.

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    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.

    Item Type: Thesis (Diploma thesis)
    Keywords: Euclidean metric, taxicab metric, maximum metric, p-metric, arc length, minimum value of pi
    Number of Pages: 24
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    asist. dr. Eva HorvatComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=12148041)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 5377
    Date Deposited: 25 Sep 2018 13:20
    Last Modified: 25 Sep 2018 13:20
    URI: http://pefprints.pef.uni-lj.si/id/eprint/5377

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