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For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

The silver constant is the algebraic number given by S = (x^3-5x^2+6x-1)_3 (1) = 2+2cos(2/7pi) (2) = 3.246979603... (3) (OEIS A116425), where (P(x))_n denotes a polynomial ...

The transcendence degree of Q(pi), sometimes called the transcendental degree, is one because it is generated by one extra element. In contrast, Q(pi,pi^2) (which is the same ...

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram ...

The Barth decic is a decic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 345. It is given by the ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...

The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...

Given two topological spaces M and N, place an equivalence relationship on the continuous maps f:M->N using homotopies, and write f_1∼f_2 if f_1 is homotopic to f_2. Roughly ...

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 ...

A classic arithmetical problem probably first posed by Euclid and investigated by various authors in the Middle Ages. The problem is formulated as a dialogue between the two ...