- Title
- Heron quadrilaterals with sides in arithmetic or geometric progression
- Creator
- Buchholz, Ralph H.; MacDougall, James A.
- Relation
- Bulletin of the Australian Mathematical Society Vol. 59, Issue 2, p. 263-269
- Publisher Link
- http://dx.doi.org/10.1017/S0004972700032883
- Publisher
- Australian Mathematical Society
- Resource Type
- journal article
- Date
- 1999
- 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.
- Subject
- number theory; 51M04; 11D25; diophantine equations; cubic and quartic equations; elementary problems in Euclidean geometries
- Identifier
- http://hdl.handle.net/1959.13/803798
- Identifier
- uon:6511
- Identifier
- ISSN:0004-9727
- Language
- eng
- Full Text
- Reviewed
- Hits: 9395
- Visitors: 6703
- Downloads: 641
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Publisher version (open access) | 273 KB | Adobe Acrobat PDF | View Details Download |