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Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

An algorithm that can be used to factor a polynomial f over the integers. The algorithm proceeds by first factoring f modulo a suitable prime p via Berlekamp's method and ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...

The number d(n) of monotone Boolean functions of n variables (equivalent to one more than the number of antichains on the n-set {1,2,...,n}) is called the nth Dedkind number. ...

A generalized Moore graph is a regular graph of degree r where the counts of vertices at each distance d=0, 1, ... from any vertex are 1, r, r(r-1), r(r-1)^2, r(r-1)^3, ..., ...

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case ...

Define the sequence a_0=1, a_1=x, and a_n=(a_(n-2))/(1+a_(n-1)) (1) for n>=0. The first few values are a_2 = 1/(1+x) (2) a_3 = (x(1+x))/(2+x) (3) a_4 = ...

The bound for the number of colors which are sufficient for map coloring on a surface of genus g, gamma(g)=|_1/2(7+sqrt(48g+1))_| is the best possible, where |_x_| is the ...