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A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy (ace)/(bdf)=1 (Honsberger 1995).

The eight of Hilbert's axioms which concern collinearity and intersection; they include the first four of Euclid's postulates.

A proper ideal of a ring that is not the intersection of two ideals which properly contain it. In a principal ideal domain, the ideal I=<a> is irreducible iff a=0 or a is an ...

A submodule N of a module M that is not the intersection of two submodules of M in which it is properly contained. In other words, for all submodules N_1 and N_2 of M, N=N_1 ...

A special ideal in a commutative ring R. The Jacobson radical is the intersection of the maximal ideals in R. It could be the zero ideal, as in the case of the integers.

A point at the intersection of two or more grid lines in a point lattice.

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

A line of constant longitude on a spheroid (or sphere). More generally, a meridian of a surface of revolution is the intersection of the surface with a plane containing the ...

If each of two nonparallel transversals with nonminimal directions meets a given curve in finite points only, then the ratio of products of the distances from the two sets of ...