Four or more points , , , , ... which lie on a Circle are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a Circle. The number of the Lattice Points which can be picked with no four concyclic is (Guy 1994).

A theorem states that if any four consecutive points of a Polygon are not concyclic, then its Area can be increased by making them concyclic. This fact arises in some Proofs that the solution to the Isoperimetric Problem is the Circle.

**References**

Guy, R. K. ``Lattice Points, No Four on a Circle.'' §F3 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, p. 241, 1994.

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1999-05-26