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An object is unique if there is no other object satisfying its defining properties. An object is said to be essentially unique if uniqueness is only referred to the ...

A mathematical structure first introduced by Kolyvagin (1990) and defined as follows. Let T be a finite-dimensional p-adic representation of the Galois group of a number ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

Let J_A, J_B, and J_C be the vertices of the outer Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

The Flint Hills series is the series S_1=sum_(n=1)^infty(csc^2n)/(n^3) (Pickover 2002, p. 59). It is not known if this series converges, since csc^2n can have sporadic large ...

A golden isozonohedron is a zonohedron all of whose faces are golden rhombi. There exist exactly five golden isozonohedra, as summarized in the following table. face count ...

The term "gradient" has several meanings in mathematics. The simplest is as a synonym for slope. The more general gradient, called simply "the" gradient in vector analysis, ...

The Haferman carpet is the beautiful fractal constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[1 1 1; 1 1 1; 1 1 1],1->[0 1 0; 1 0 1; ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be harmonic if 1/a+1/c=2/b. In particular, such a triple is harmonic if the reciprocals of its terms form an ...

The hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 ...