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 sides, (where is the Area) satisfies a Monic Polynomial of degree , where
(1) | |||
(2) |
For Triangles
, the Polynomial is Heron's Formula, which may be written
(3) |
(4) |
See also Concyclic, Cyclic Hexagon, Cyclic Pentagon, Cyclic Quadrangle, Cyclic Quadrilateral
References
Robbins, D. P. ``Areas of Polygons Inscribed in a Circle.'' Discr. Comput. Geom. 12, 223-236, 1994.
Robbins, D. P. ``Areas of Polygons Inscribed in a Circle.'' Amer. Math. Monthly 102, 523-530, 1995.
Sloane, N. J. A. Sequence
A000531
in ``The On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html.
© 1996-9 Eric W. Weisstein