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A game played on a board of a given shape consisting of a number of holes of which all but one are initially filled with pegs. The goal is to remove all pegs but one by ...

The Hurwitz zeta function zeta(s,a) is a generalization of the Riemann zeta function zeta(s) that is also known as the generalized zeta function. It is classically defined by ...

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...

The Hilbert curve is a Lindenmayer system invented by Hilbert (1891) whose limit is a plane-filling function which fills a square. Traversing the polyhedron vertices of an ...

The word "surface" is an important term in mathematics and is used in many ways. The most common and straightforward use of the word is to denote a two-dimensional ...

The Farey sequence F_n for any positive integer n is the set of irreducible rational numbers a/b with 0<=a<=b<=n and (a,b)=1 arranged in increasing order. The first few are ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

Johnson solid J_4. The bottom eight polyhedron vertices are (+/-1/2(1+sqrt(2)),+/-1/2,0),(+/-1/2,+/-1/2(1+sqrt(2)),0), and the top four polyhedron vertices are ...

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 ...

Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) ...