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A technical mathematical object defined in terms of a polynomial ring of n variables over a field k. Syzygies occur in tensors at rank 5, 7, 8, and all higher ranks, and play ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...

The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...

The logarithmic integral (in the "American" convention; Abramowitz and Stegun 1972; Edwards 2001, p. 26), is defined for real x as li(x) = {int_0^x(dt)/(lnt) for 0<x<1; ...

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

65537 is the largest known Fermat prime, and the 65537-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. The 65537-gon has so many ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

Borsuk conjectured that it is possible to cut an n-dimensional shape of generalized diameter 1 into n+1 pieces each with diameter smaller than the original. It is true for ...

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...