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Viviani's theorem and its generalizations

Terezija Ceferin (2016) Viviani's theorem and its generalizations. MSc thesis.

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    Abstract

    The present master’s thesis deals with Viviani’s theorem valid in an equilateral triangle and stating that the sum of the distances between any interior point and the sides equals the triangle’s altitude i.e. that the sum of the distances is constant. In the paper it is investigated whether the sum of the distances from an interior point to the sides of a nonequilateral triangle also equals any of the triangle’s altitudes or whether there exists any other relation between the sum of the distances and the altitudes. A further investigation refers to a generalisation of the theorem to other polygons and polyhedra. The generalisation concept on chosen examples is shown by the use of various methods. To this end, convex and concave polygons (or polyhedra) are investigated separately. The conclusion gives concrete examples of dealing with the theorem in class and an example of its use in the drawing of diagrams having the form of an equilateral triangle.

    Item Type: Thesis (MSc thesis)
    Keywords: Viviani’s theorem, equilateral triangle, constant Viviani sum property (CVS property), isosum segment, isosum cross section, convex polygon, convex polyhedron
    Number of Pages: 75
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    red. prof. dr. Dušan RepovšMentor
    red. prof. dr. Matija CenceljComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11340873)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 4174
    Date Deposited: 24 Nov 2016 14:02
    Last Modified: 24 Nov 2016 14:02
    URI: http://pefprints.pef.uni-lj.si/id/eprint/4174

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