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Given a group with elements A and X, there must be an element B which is a similarity transformation of A,B=X^(-1)AX so A and B are conjugate with respect to X. Conjugate ...

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

The epispiral is a plane curve with polar equation r=asec(ntheta). There are n sections if n is odd and 2n if n is even. A slightly more symmetric version considers instead ...

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) = ...

Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a ...