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Two figures are said to be similar when all corresponding angles are equal, and are directly similar when all corresponding angles are equal and described in the same ...

The Dirichlet lambda function lambda(x) is the Dirichlet L-series defined by lambda(x) = sum_(n=0)^(infty)1/((2n+1)^x) (1) = (1-2^(-x))zeta(x), (2) where zeta(x) is the ...

A series suma(n)e^(-lambda(n)z), where a(n) and z are complex and {lambda(n)} is a monotonic increasing sequence of real numbers. The numbers lambda(n) are called the ...

kappa(d)={(2lneta(d))/(sqrt(d)) for d>0; (2pi)/(w(d)sqrt(|d|)) for d<0, (1) where eta(d) is the fundamental unit and w(d) is the number of substitutions which leave the ...

A.k.a. the pigeonhole principle. Given n boxes and m>n objects, at least one box must contain more than one object. This statement has important applications in number theory ...

Dirichlet's principle, also known as Thomson's principle, states that there exists a function u that minimizes the functional D[u]=int_Omega|del u|^2dV (called the Dirichlet ...

A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space ...

A discrete group is a topological group with the discrete topology. Often in practice, discrete groups arise as discrete subgroups of continuous Lie groups acting on a ...

Let G be an algebraic group. G together with the discrete topology is a locally compact group and one may consider the counting measure as a left invariant Haar measure on G. ...