Search Results for ""

The map which takes points on the surface of a sphere S^2 to their antipodal points.

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

A half-plane is a planar region consisting of all points on one side of an infinite straight line, and no points on the other side. If the points on the line are included, ...

If intersecting stable and unstable manifolds (separatrices) emanate from fixed points of different families, they are called heteroclinic points.

A circle having a given number of lattice points on its circumference. The Schinzel circle having n lattice points is given by the equation {(x-1/2)^2+y^2=1/45^(k-1) for n=2k ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

Geometric objects lying in a common plane are said to be coplanar. Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar iff the ...

Let A_1, A_2, A_3, and A_4 be four points on a circle, and H_1, H_2, H_3, H_4 the orthocenters of triangles DeltaA_2A_3A_4, etc. If, from the eight points, four with ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...