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Heron Quadrilaterals with Sides in Arithmetic or Geometric Progression

Buchholz, Ralph H. and MacDougall, James A. (1999) Heron Quadrilaterals with Sides in Arithmetic or Geometric Progression. Bulletin of Australian Mathematical Society, 59 . pp. 263-269.

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    Abstract

    We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterization is given for the infinite family of triangles with sides in arithmetic progression. We show that there are no triangles with sides in geometric progression. We also show that apart from the square there are no cyclic quadrilaterals whose sides form either a geometric or an arithmetic progression. The solution of both quadrilateral cases involves searching for rational points on certain elliptic curves.

    Item Type: Article
    Subjects: 00-xx General
    Faculty: UNSPECIFIED
    Depositing User: Stephanie
    Date Deposited: 18 Nov 2010 12:07
    Last Modified: 18 Nov 2010 12:07
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/827

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