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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 ...

An affine transformation in which the scale is reduced.

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.

Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.

Two figures are homothetic if they are related by a dilation (a dilation is also known as a homothecy). This means that the connectors of corresponding points are concurrent ...

A figure resembling a daisy or sunflower in which copies of a geometric figure of increasing size are placed at regular intervals along a spiral. The resulting figure appears ...

A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological ...

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...

There are at least two meanings on the word congruent in mathematics. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry ...

A finite set of contraction maps w_i for i=1, 2, ..., N, each with a contractivity factor s<1, which map a compact metric space onto itself. It is the basis for fractal image ...