Cyclic polygons with rational sides and area Original Research Article

We generalise the notion of Heron triangles to rational-sided, cyclic n-gons with rational area using Brahmaguptaʹs formula for the area of a cyclic quadrilateral and Robbinsʹ 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.