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A uniform-density polyhedral solid is unistable (also called monostable) if it is stable on exactly one face (Croft et al. 1991, p. 61). For example, the 19-faced polyhedron ...

Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...

An equilibrium minimal surface for a crystal or drop which has the least anisotropic surface free energy for a given volume. It is the anisotropic analog of a sphere. In the ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

Place a point somewhere on a line segment. Now place a second point and number it 2 so that each of the points is in a different half of the line segment. Continue, placing ...

The (interior) bisector of an angle, also called the internal angle bisector (Kimberling 1998, pp. 11-12), is the line or line segment that divides the angle into two equal ...

Given a point with trilinear coordinates P=alpha:beta:gamma, the anticevian triangle DeltaA^'B^'C^' of a triangle DeltaABC with respect to P is a triangle such that 1. B^'C^' ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More ...

A polyhedron is said to be canonical if all its polyhedron edges touch a sphere and the center of gravity of their contact points is the center of that sphere. In other ...