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A random polygon containing the origin (Kovalenko 1999).

The edge of a polygon or face of a polyhedron are sometimes called sides.

Except for triangles, every simple polygon has at least two nonoverlapping ears.

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

A conformal mapping from the upper half-plane to a polygon.

A real-valued function g defined on a convex subset C subset R^n is said to be quasi-concave if for all real alpha in R, the set {x in C:g(x)>=alpha} is convex. This is ...

The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...

Connectivity properties obey the following hierarchy: convex => star convex => pathwise-connected => connected.

A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with ...

A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave. If P(x) is log-convex and Q(x) is unimodal, ...