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The Kirchhoff index Kf, also simply called the resistance and denoted R (Lukovits et al. 1999), of a connected graph G on n nodes is defined by ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

The Barnette-Bosák-Lederberg graph is a graph on 38 vertices which is the smallest known example of a planar 3-connected nonhamiltonian graph, i.e., the smallest known ...