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The Machin-like formula 1/4pi=12cot^(-1)18+8cot^(-1)57-5cot^(-1)239.

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

A formula of first-order logic is said to be in Skolemized form (sometimes also called Skolem standard form or universal form) if it is of the form forall x_1... forall x_nM, ...

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

The functions (also called the circular functions) comprising trigonometry: the cosecant cscx, cosine cosx, cotangent cotx, secant secx, sine sinx, and tangent tanx. However, ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

The hyperbolic functions sinhz, coshz, tanhz, cschz, sechz, cothz (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and ...

For |q|<1, the Rogers-Ramanujan identities are given by (Hardy 1999, pp. 13 and 90), sum_(n=0)^(infty)(q^(n^2))/((q)_n) = 1/(product_(n=1)^(infty)(1-q^(5n-4))(1-q^(5n-1))) ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...