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Sphere line picking is the selection of pairs of points corresponding to vertices of a line segment with endpoints on the surface of a sphere. n random line segments can be ...

The Thomson problem is to determine the stable equilibrium positions of n classical electrons constrained to move on the surface of a sphere and repelling each other by an ...

Given a triangle with one vertex at the origin and the others at positions v_1 and v_2, one might think that a random point inside the triangle would be given by ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...

Geometry

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

Ball triangle picking is the selection of triples of points (corresponding to vertices of a general triangle) randomly placed inside a ball. n random triangles can be picked ...

A convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities mx<=b, where m is a real s×3 matrix and b is a real s-vector. ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...