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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 ...

The radius of a polygon's incircle or of a polyhedron's insphere, denoted r or sometimes rho (Johnson 1929). A polygon possessing an incircle is same to be inscriptable or ...

A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

A principal vertex x_i of a simple polygon P is called a mouth if the diagonal [x_(i-1),x_(i+1)] is an extremal diagonal (i.e., the interior of [x_(i-1),x_(i+1)] lies in the ...

A skew polygon such that every two consecutive sides (but no three) belong to a face of a regular polyhedron. Every regular polyhedron can be orthogonally projected onto a ...

That portion of geometry dealing with figures in a plane, as opposed to solid geometry. Plane geometry deals with the circle, line, polygon, etc.

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

The recurrence relation E_n=E_2E_(n-1)+E_3E_(n-2)+...+E_(n-1)E_2 which gives the solution to Euler's polygon division problem.

A perimeter-bisecting line segment which originates at a vertex of a polygon. The three splitters of a triangle concur in a point known as the Nagel point Na.