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A transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving ...

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

A mathematical relationship transforming a function f(x) to the form f(x+a).

Two geometric figures are said to exhibit geometric congruence (or "be geometrically congruent") iff one can be transformed into the other by an isometry (Coxeter and ...

A geometric sequence is a sequence {a_k}, k=0, 1, ..., such that each term is given by a multiple r of the previous one. Another equivalent definition is that a sequence is ...

A point-to-line and line-to-point transformation which transforms points A into lines a^' and lines b into points B^' such that a^' passes through B^' iff A^' lies on b.

A perspective collineation in which the center and axis are not incident. The term was first used by Poncelet (Cremona 1960, p. ix).

The geometric mean of a sequence {a_i}_(i=1)^n is defined by G(a_1,...,a_n)=(product_(i=1)^na_i)^(1/n). (1) Thus, G(a_1,a_2) = sqrt(a_1a_2) (2) G(a_1,a_2,a_3) = ...

A one-dimensional geometric object such as a pencil or line segment range.

A triple (a,b,c) of positive integers satisfying a<b<c is said to be geometric if ac=b^2. In particular, such a triple is geometric if its terms form a geometric sequence ...