Search Results for ""

Number Theory

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

The Mathieu functions are the solutions to the Mathieu differential equation (d^2V)/(dv^2)+[a-2qcos(2v)]V=0. (1) Even solutions are denoted C(a,q,v) and odd solutions by ...

A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

Because even high-resolution computer monitors have a relatively small number of pixels, when graphics or text display distinguish between individual pixels. The result is ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

Consider the excircles J_A, J_B, and J_C of a triangle, and the external Apollonius circle Gamma tangent externally to all three. Denote the contact point of Gamma and J_A by ...

Successive application of Archimedes' recurrence formula gives the Archimedes algorithm, which can be used to provide successive approximations to pi (pi). The algorithm is ...

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...