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An algorithm for computing an Egyptian fraction.

The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

A series is called artistic if every three consecutive terms have a common three-way ratio P[a_i,a_(i+1),a_(i+2)]=((a_i+a_(i+1)+a_(i+2))a_(i+1))/(a_ia_(i+2)). A series is ...

A convex planar domain in which the minimal generalized diameter is >1 always contains a circle of radius 1/3.

Given a geometric sequence {a_1,a_1r,a_1r^2,...}, the number r is called the common ratio associated to the sequence.

The five of Hilbert's axioms which concern geometric equivalence.

If the lines joining corresponding points of two directly similar figures are divided proportionally, then the locus of the points of the division will be a figure directly ...

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

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

A similarity transformation which preserves orientation, also called a homothety.