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Cyclic Polygons with Rational Sides and Area

MacDougall, James A. and Buchholz, Ralph H. (2008) Cyclic Polygons with Rational Sides and Area. Journal of Number Theory, 128 (1). pp. 17-48.

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    Abstract

    We generalise the notion of Heron triangles to rational-sided, cyclic $n$-gons with rational area using Brahmagupta's formula for the area of a cyclic quadrilateral and Robbins' formul$\ae$ for the area of cyclic pentagons and hexagons. We use approximate techniques to explore rational area $n$-gons for n greater than six. Finally, we produce a method of generating non-Eulerian rational area cyclic $n$-gons for even $n$ and conjecturally classify all rational area cyclic $n$-gons.

    Item Type: Article
    Subjects: 00-xx General > 00Axx General and miscellaneous specific topics
    Faculty: UNSPECIFIED
    Depositing User: Stephanie
    Date Deposited: 16 Nov 2010 15:16
    Last Modified: 16 Nov 2010 15:16
    URI: http://docserver.carma.newcastle.edu.au/id/eprint/785

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