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The orthocubic (or ortho cubic) Z(X_4) is a self-isogonal cubic with pivot point at the orthocenter H, so it has parameter x=cosBcosC and trilinear equation (Cundy and Parry ...

The two-argument Ramanujan function is defined by phi(a,n) = 1+2sum_(k=1)^(n)1/((ak)^3-ak) (1) = 1-1/a(H_(-1/a)+H_(1/a)+2H_n-H_(n-1/a)-H_(n+1/a)). (2) The one-argument ...

The reflexive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same reflexive closure as R. Thus aR^'b for any elements a and b of X, ...

The direct product of the rings R_gamma, for gamma some index set I, is the set product_(gamma in I)R_gamma={f:I-> union _(gamma in I)R_gamma|f(gamma) in R_gamma all gamma in ...

A condition used in the definition of a mathematical object, commonly denoted : or |. For example, the rationals Q can be defined by Q={p/q:q!=0,p,q in Z}, read as "the set ...

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...

A system in which a strange loop appears.

Every nonempty set of positive integers contains a smallest member.

The negative integers ..., -3, -2, -1.

A doubly stochastic matrix is a matrix A=(a_(ij)) such that a_(ij)>=0 and sum_(i)a_(ij)=sum_(j)a_(ij)=1 is some field for all i and j. In other words, both the matrix itself ...