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The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...

An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles arise in both number fields and function fields. The ...

Let f(z) be a transcendental meromorphic function, and let D_1, D_2, ..., D_5 be five simply connected domains in C with disjoint closures (Ahlfors 1932). Then there exists j ...

Ai(z) and Ai^'(z) have zeros on the negative real axis only. Bi(z) and Bi^'(z) have zeros on the negative real axis and in the sector pi/3<|argz|<pi/2. The nth (real) roots ...

A number n is called amenable if it can be built up from integers a_1, a_2, ..., a_k by either addition or multiplication such that sum_(i=1)^na_i=product_(i=1)^na_i=n (1) ...

A flow defined analogously to the Anosov diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only ...

An Archimedean circle is a circle defined in the arbelos in a natural way and congruent to Archimedes' circles, i.e., having radius rho=1/2r(1-r) for an arbelos with outer ...

Successive application of Archimedes' recurrence formula gives the Archimedes algorithm, which can be used to provide successive approximations to pi (pi). The algorithm is ...