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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 ...An affine transformation in which the scale is reduced.

If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a

**geometric**realization of S, and is uniquely ...The

**geometric**span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed ......