A Robbins Pentagon

A Robbins pentagon is a cyclic polygon with 5 integer sides and integer area. The one shown above is the one with the smallest area amongst those with five distinct sides. It also has the property that all its diagonals are rational which means that it can be decomposed into Heron triangles. The converse is not necessarily true---namely, three Heron triangles cannot always be glued together in such a way that their exterior vertices lie on a circle. It is unknown whether or not an indecomposible Robbins pentagon exists.

See Cyclic polygons for more details.

[ See also Eric Weisstein's excellent web page on this topic.]

Ralph Buchholz

05 September 2008