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Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...

The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

The wallpaper groups are the 17 possible plane symmetry groups. They are commonly represented using Hermann-Mauguin-like symbols or in orbifold notation (Zwillinger 1995, p. ...

A subset B of a vector space E is said to be absorbing if for any x in E, there exists a scalar lambda>0 such that x in muB for all mu in F with |mu|>=lambda, where F is the ...

In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse ...

The term used in propositional calculus for the NAND connective. The notation A|B is used for this connective, a most unfortunate choice in light of modern usage of A|B or ...