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A Lorentz transformation is a four-dimensional transformation x^('mu)=Lambda^mu_nux^nu, (1) satisfied by all four-vectors x^nu, where Lambda^mu_nu is a so-called Lorentz ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...

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 ...

The Buffon-Laplace needle problem asks to find the probability P(l,a,b) that a needle of length l will land on at least one line, given a floor with a grid of equally spaced ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...

The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

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 ...

The Reuleaux tetrahedron, sometimes also called the spherical tetrahedron, is the three-dimensional solid common to four spheres of equal radius placed so that the center of ...