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The dihedral group D_2 is a point group that is isomorphic to the vierergruppe and the finite group C_2×C_2.

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

If (f,U) and (g,V) are functions elements, then (g,V) is a direct analytic continuation of (f,U) if U intersection V!=emptyset and f and g are equal on U intersection V.

The direction from an object A to another object B can be specified as a vector v=AB^-> with tail at A and head at B. However, since this vector has length equal to the ...

The curve d(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u).

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...

Two sets A_1 and A_2 are disjoint if their intersection A_1 intersection A_2=emptyset, where emptyset is the empty set. n sets A_1, A_2, ..., A_n are disjoint if A_i ...

A generalization by Kronecker of Kummer's theory of prime ideal factors. A divisor on a full subcategory C of mod(A) is an additive mapping chi on C with values in a ...

A number of attractive 11-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...