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Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...

If r is an algebraic number of degree n, then the totality of all expressions that can be constructed from r by repeated additions, subtractions, multiplications, and ...

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

There are two kinds of Bell polynomials. A Bell polynomial B_n(x), also called an exponential polynomial and denoted phi_n(x) (Bell 1934, Roman 1984, pp. 63-67) is a ...

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

A positive integer n is called a base-b Rhonda number if the product of the base-b digits of n is equal to b times the sum of n's prime factors. These numbers were named by ...

The Jackson-Slater identity is the q-series identity of Rogers-Ramanujan-type given by sum_(k=0)^(infty)(q^(2k^2))/((q)_(2k)) = ...

The base-4 method of counting in which only the digits 0, 1, 2, and 3 are used. The illustration above shows the numbers 0 to 63 represented in quaternary, and the following ...

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...