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For a polynomial P(x_1,x_2,...,x_k), the Mahler measure of P is defined by (1) Using Jensen's formula, it can be shown that for P(x)=aproduct_(i=1)^(n)(x-alpha_i), ...

The term Nasik cube can refer to a number of different sorts of magic cubes. In particular, a Nasik cube is a magic cube in which additionally 1. The broken space diagonals ...

Polynomials O_n(x) that can be defined by the sum O_n(x)=1/4sum_(k=0)^(|_n/2_|)(n(n-k-1)!)/(k!)(1/2x)^(2k-n-1) (1) for n>=1, where |_x_| is the floor function. They obey the ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

The pentagonal wegde is one of the seven topologically distinct convex hexahedra. Like the cube, it contains 8 vertices, 12 edges, and 6 faces, but its faces consist of 2 ...

A polyform of 30-60-90 triangles. The name was coined by Ed Pegg, Jr. because of the 30-60-90 triangle's use in mechanical drawing and drafting. The Eternity puzzle is based ...

Quantile-quantile plots (also called q-q plots) are used to determine if two data sets come from populations with a common distribution. In such a plot, points are formed ...

A polynomial given in terms of the Neumann polynomials O_n(x) by S_n(x)=(2xO_n(x)-2cos^2(1/2npi))/n.

The p×p square matrix formed by setting s_(ij)=xi^(ij), where xi is a pth root of unity. The Schur matrix has a particularly simple determinant given by ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...