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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.

A star polygon-like figure {p/q} for which p and q are not relatively prime. Examples include the hexagram {6/2}, star of Lakshmi {8/2}, and nonagram {9/3}.

A fractal composed of repeated copies of a pentagram or other polygon. The above figure shows a generalization to different offsets from the center.

A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a ...