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A number n is called a barrier of a number-theoretic function f(m) if, for all m<n, m+f(m)<=n. Neither the totient function phi(n) nor the divisor function sigma(n) has a ...

A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness ...

The function defined by the contour integral J_(n,k)(z) =1/(2pii)int^((0+))t^(-n-1)(t+1/t)^kexp[1/2z(t-1/t)]dt, where int_((0+)) denotes the contour encircling the point z=0 ...

An Cesàro equation is a natural equation which expresses a curve in terms of its arc length function s(t) and radius of curvature rho(t) (or equivalently, the curvature ...

The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from ...

The point on the positive ray of the normal vector at a distance rho(s), where rho is the radius of curvature. It is given by z = x+rhoN (1) = x+rho^2(dT)/(ds), (2) where N ...

The Danzer configuration is a 35_4 self-dual configuration of 35 lines and 35 points in which 4 points lie on each line and 4 lines pass through each point. The Levi graph of ...

Two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through ...

A group action G×X->X is effective if there are no trivial actions. In particular, this means that there is no element of the group (besides the identity element) which does ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...