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A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths b ...

How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular ...

"Analysis of Variance." A statistical test for heterogeneity of means by analysis of group variances. ANOVA is implemented as ANOVA[data] in the Wolfram Language package ...

Specifying two adjacent side lengths a and c of a triangle (with a<c) and one acute angle A opposite a does not, in general, uniquely determine a triangle. If sinA<a/c, there ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

The Alexander invariant H_*(X^~) of a knot K is the homology of the infinite cyclic cover of the complement of K, considered as a module over Lambda, the ring of integral ...

An antelope graph (Jelliss 2019) is a graph formed by all possible moves of a hypothetical chess piece called an "antelope" which moves analogously to a knight except that it ...

A square matrix A is antihermitian if it satisfies A^(H)=-A, (1) where A^(H) is the adjoint. For example, the matrix [i 1+i 2i; -1+i 5i 3; 2i -3 0] (2) is an antihermitian ...

Any square matrix A can be written as a sum A=A_S+A_A, (1) where A_S=1/2(A+A^(T)) (2) is a symmetric matrix known as the symmetric part of A and A_A=1/2(A-A^(T)) (3) is an ...

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only ...