- Title
- Cyclic polygons with rational sides and area
- Creator
- Buchholz, Ralph H.; MacDougall, James A.
- Relation
- Journal of Number Theory Vol. 128, Issue 1, p. 17-48
- Publisher Link
- http://dx.doi.org/10.1016/j.jnt.2007.05.005
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2008
- Description
- 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' formulæ 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.
- Subject
- Heron triangle; rational polygon; cyclic polygon; rational area
- Identifier
- http://hdl.handle.net/1959.13/41712
- Identifier
- uon:4922
- Identifier
- ISSN:0022-314X
- Language
- eng
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