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An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of ...

Given a subset S subset R^n and a real function f which is Gâteaux differentiable at a point x in S, f is said to be pseudoconvex at x if del f(x)·(y-x)>=0,y in ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

The collapsoids are a class of non-convex collapsible polyhedra. They can be constructed by replacing each edge of a dodecahedron or icosahedron by the diagonal of a pyramid ...

The problem of finding in how many ways E_n a plane convex polygon of n sides can be divided into triangles by diagonals. Euler first proposed it to Christian Goldbach in ...

Given a convex plane region with area A and perimeter p, A-1/2p<N<=A+1/2p+1, where N is the number of enclosed lattice points (Nosarzewska 1948). This improves on Jarnick's ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

There are least two Bang's theorems, one concerning tetrahedra (Bang 1897), and the other with widths of convex domains (Bang 1951). The theorem of Bang (1897) states that ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

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 ...