A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. Since every triangle has a circumcircle, every triangle is cyclic. It is conjectured that for a cyclic polygon of 2m + 1 sides, 16K^2 (where K is the area) satisfies a monic polynomial of degree Δ_m, where Δ_m | congruent | sum_(k = 0)^(m - 1)(m - k)(2m + 1 k) | = | 1/2[(2m + 1)(2m m) - 2^(2m)] (Robbins 1995). It is also conjectured that a cyclic polygon with 2m + 2 sides satisfies one of two polynomials of degree Δ_m. The first few values of Δ_m are 1, 7, 38, 187, 874, ... (OEIS A000531).

concyclic | cyclic hexagon | cyclic pentagon | cyclic quadrangle | cyclic quadrilateral | Japanese theorem