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Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

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

The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral ...

A sphere is defined as the set of all points in three-dimensional Euclidean space R^3 that are located at a distance r (the "radius") from a given point (the "center"). Twice ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...