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Hippopede and its related curves

Katja Stojnšek (2015) Hippopede and its related curves. Diploma thesis.

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    Abstract

    The thesis presents a plane curve, called hippopede and its related curves, which can arise in different ways. Hippopede is a plane algebraic quartic curve. It is often known as the hippopede of Proclus, after Proclus who was the first to study it and also the curve of Booth because of work done on it by J. Booth. Hippopede is the intersection of a torus with one of its tangent planes, that is a plane parallel to its rotational symmetry axis. These curves named as Perseus curves or spiric sections, were first described by the ancient Greek geometer Perseus. The curve takes any of a variety of forms depending on where the donut is sliced. It may bee an elliptical lemniscate of Booth, a hyperbolic lemniscate of Booth, a figure eight curve or a lemniscate of Bernoulli. The aim of the thesis is to examine the hippopede and her related plane curves with properities of them. Here are a lot of pictures, sometimes in 3D and in that time are naturally welcome 3D glasses. In the conclusion are presented the key links of dealt curves and the discussion about that in primary and secondary school. Possibilities of the application are presented using program of dynamic geometry GeoGebra in two and in three dimensional space. Because this new program is very fresh, it can give us even more interesting lessons.

    Item Type: Thesis (Diploma thesis)
    Keywords: conic section, plane curve, pedal curve, hippopede, lemniscate, space curves, homothetic transformation, Cassini’s ovals
    Number of Pages: 67
    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=10598217)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 2873
    Date Deposited: 01 Jul 2015 08:19
    Last Modified: 01 Jul 2015 08:19
    URI: http://pefprints.pef.uni-lj.si/id/eprint/2873

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