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Tractrix

Nadja Apšner (2016) Tractrix. Diploma thesis.

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    Abstract

    The diploma thesis presents a transcendent plane curve, called tractrix, and its related curves. On the plane the tractrix is defined by a dotted mass that is attached to the tensile nor constant size, the free end is drawn by the straight line in that plane. This is usually a straight line abscissa. The purpose of this diploma thesis is to thoroughly study the tractrix. For this purpose there are basic descriptions of it and in connection also made calculations of the area, arc lenght, area of the surface and volume, which we get with rotating tractrix around it’s asymptote. The surface is called pseudosphere and it has a constant negative Gaussian curvature. Described is also the emergence of the tractrix with simple mechanical tools and the creation of a model of pseudosphere. In conclusion there are being presented different formations of tractrix and also connections with others curves.

    Item Type: Thesis (Diploma thesis)
    Keywords: plane curve, tangent, tractrix, polar tractrix, curvature, evolute, pseudosphere, pedal curve
    Number of Pages: 63
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko RazpetMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11069257)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 3545
    Date Deposited: 07 Jul 2016 14:03
    Last Modified: 07 Jul 2016 14:03
    URI: http://pefprints.pef.uni-lj.si/id/eprint/3545

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