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A cyclotomic field Q(zeta) is obtained by adjoining a primitive root of unity zeta, say zeta^n=1, to the rational numbers Q. Since zeta is primitive, zeta^k is also an nth ...

A differential k-form omega of degree p in an exterior algebra ^ V is decomposable if there exist p one-forms alpha_i such that omega=alpha_1 ^ ... ^ alpha_p, (1) where alpha ...

A subspace A of X is called a deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X and a in A, 1. F(x,0)=x, 2. F(x,1) in A, ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

The disdyakis dodecahedron is the dual polyhedron of the Archimedean great rhombicuboctahedron A_3 and Wenninger dual W_(15). It is also called the hexakis octahedron ...

For any Abelian group G and any natural number n, there is a unique space (up to homotopy type) such that all homotopy groups except for the nth are trivial (including the ...

G_(ab)=R_(ab)-1/2Rg_(ab), where R_(ab) is the Ricci curvature tensor, R is the scalar curvature, and g_(ab) is the metric tensor. (Wald 1984, pp. 40-41). It satisfies ...

Fano's geometry is a finite geometry attributed to Fano from around the year 1892. This geometry comes with five axioms, namely: 1. There exists at least one line. 2. Every ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

Four line geometry is a finite geometry subject to the following three axioms: 1. there exist exactly four lines, 2. any two distinct lines have exactly one point of on both ...