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The corkscrew surface, sometimes also called the twisted sphere (Gray 1997, p. 477), is a surface obtained by extending a sphere along a diameter and then twisting. It can be ...

A family gamma of nonempty subsets of X whose union contains the given set X (and which contains no duplicated subsets) is called a cover (or covering) of X. For example, ...

The cubeplex graph is the cubic Hamiltonian graph on 12 nodes illustrated above in several embeddings and corresponding to the graph Gamma_1 in Fischer and Little (2001). It ...

A similarity transformation which transforms each line to a parallel line whose length is a fixed multiple of the length of the original line. The simplest dilation is ...

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 ...

Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...

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) = ...

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...