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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/803798

Title: Heron quadrilaterals with sides in arithmetic or geometric progression
Author/Creator: Buchholz, Ralph H.; MacDougall, James A.
Description: 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.
Relation: Bulletin of the Australian Mathematical Society Vol. 59, Issue 2, p. 263-269
Publisher Link: http://dx.doi.org/10.1017/S0004972700032883
Date: 1999
Publisher: Australian Mathematical Society
Keyword(s): number theory; 51M04; 11D25; diophantine equations; cubic and quartic equations; elementary problems in Euclidean geometries
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/803798
Identifier: ISSN:0004-9727
Language: eng

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