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The rascal triangle is a number triangle with numbers arranged in staggered rows such that a_(n,r)=n(r-n)+1. (1) The published study of this triangle seems to have originated ...

Frey's theorem states that every Abelian category is a subcategory of some category of modules over a ring. Mitchell (1964) has strengthened this, saying every Abelian ...

The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...

Given a square complex or real matrix A, a matrix norm ||A|| is a nonnegative number associated with A having the properties 1. ||A||>0 when A!=0 and ||A||=0 iff A=0, 2. ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

An almost unit is a nonunit in the integral domain of formal power series with a nonzero first coefficient, P=a_1x+a_2x^2+..., where a_1!=0. Under the operation of ...

Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z. (1) Real numbers are associative under addition ...

An augmented polyhedron is a polyhedron formed from a base polyhedron via the augmentation operation on one or more of its faces. Augmentation is implemented under the ...