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Consider n intersecting circles. The maximal number of regions into which these divide the plane are N(n)=n^2-n+2, giving values for n=1, 2, ... of 2, 4, 8, 14, 22, 32, 44, ...

The conjecture due to Pollock (1850) that every number is the sum of at most five tetrahedral numbers (Dickson 2005, p. 23; incorrectly described as "pyramidal numbers" and ...

Let n be a positive integer and r(n) the number of (not necessarily distinct) prime factors of n (with r(1)=0). Let O(m) be the number of positive integers <=m with an odd ...

The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a ...

An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is O(n^k) for some nonnegative integer k, ...

A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the ...

A number satisfying Fermat's little theorem (or some other primality test) for some nontrivial base. A probable prime which is shown to be composite is called a pseudoprime ...

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

The projective plane crossing number of a graph is the minimal number of crossings with which the graph can be drawn on the real projective plane. A graph with projective ...

The path traced out by a fixed point at a radius b>a, where a is the radius of a rolling circle, also sometimes called an extended cycloid. The prolate cycloid contains ...