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The 13 Archimedean dual graphs are the skeletons of the Archimedean dual solids, illustrated above. Since they are polyhedral graphs, they are also planar. However, none of ...

The first few terms of the continued fraction of the Copeland-Erdős constant are [0; 4, 4, 8, 16, 18, 5, 1, ...] (OEIS A030168), illustrated above. Interestingly, while the ...

A quantity from which another (the subtrahend) is subtracted.

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

For every k>=1, let C_k be the set of composite numbers n>k such that if 1<a<n, GCD(a,n)=1 (where GCD is the greatest common divisor), then a^(n-k)=1 (mod n). Special cases ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

There appear to be two different definitions of the standard error. The standard error of a sample of sample size n is the sample's standard deviation divided by sqrt(n). It ...

A pairing function is a function that reversibly maps Z^*×Z^* onto Z^*, where Z^*={0,1,2,...} denotes nonnegative integers. Pairing functions arise naturally in the ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...