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The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

Porter's constant is the constant appearing in formulas for the efficiency of the Euclidean algorithm, C = (6ln2)/(pi^2)[3ln2+4gamma-(24)/(pi^2)zeta^'(2)-2]-1/2 (1) = ...

The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), ...

Determination of whether predicate P(x_1,...,x_n) is true or false for any given values of x_1, ..., x_n is called its decision problem. The decision problem for predicate ...

The extension ring obtained from a commutative unit ring (other than the trivial ring) when allowing division by all non-zero divisors. The ring of fractions of an integral ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

Saalschütz's theorem is the generalized hypergeometric function identity _3F_2[a,b,-n; c,1+a+b-c-n;1]=((c-a)_n(c-b)_n)/((c)_n(c-a-b)_n) (1) which holds for n a nonnegative ...

The sample variance m_2 (commonly written s^2 or sometimes s_N^2) is the second sample central moment and is defined by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ the ...