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Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

The discrete uniform distribution is also known as the "equally likely outcomes" distribution. Letting a set S have N elements, each of them having the same probability, then ...

A number n is called an Egyptian number if it is the sum of the denominators in some unit fraction representation of a positive whole number not consisting entirely of 1s. ...

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...

Elliptic alpha functions relate the complete elliptic integrals of the first K(k_r) and second kinds E(k_r) at elliptic integral singular values k_r according to alpha(r) = ...

A cone with elliptical cross section. The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a(h-u)/hcosv (1) y = ...

The elliptic hyperboloid is the generalization of the hyperboloid to three distinct semimajor axes. The elliptic hyperboloid of one sheet is a ruled surface and has Cartesian ...

The first singular value k_1 of the elliptic integral of the first kind K(k), corresponding to K^'(k_1)=K(k_1), (1) is given by k_1 = 1/(sqrt(2)) (2) k_1^' = 1/(sqrt(2)). (3) ...

The Engel polyhedra are two 38-faced plesiohedra (and hence space-filling) discovered by Engel (Engel 1981; Engel 1986, p. 220; Grünbaum and Shephard 1980; Senechal 1990, ...

A version of the liar's paradox, attributed to the philosopher Epimenides in the sixth century BC. "All Cretans are liars... One of their own poets has said so." This is not ...