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An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

Consider a power series in a complex variable z g(z)=sum_(n=0)^inftya_nz^n (1) that is convergent within the open disk D:|z|<R. Convergence is limited to within D by the ...

Let F,G:C->D be functors between categories C and D. A natural transformation Phi from F to G consists of a family Phi_C:F(C)->G(C) of morphisms in D which are indexed by the ...

The primes nearest to the nonnegative integers n=0, 1, 2, ..., assigning ties to the smaller prime, are 2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, ... (OEIS A051697). If ...

Let C be an error-correcting code consisting of N codewords in which each codeword consists of n letters taken from an alphabet A of length q, and every two distinct ...

A real quantity having a value less than zero (<0) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Samuel Pepys wrote Isaac Newton a long letter asking him to determine the probabilities for a set of dice rolls related to a wager he planned to make. Pepys asked which was ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...