Noun
hyperplane (plural hyperplanes)
(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)
As a 3-sphere moves through a given three-dimensional hyperplane, the intersection starts out as a point, then becomes a growing 2-sphere that reaches its maximal size when the hyperplane cuts right through the "equator" of the 3-sphere. Source: Internet
A linear subspace that contains all elements but one of a basis of the ambient space is a vector hyperplane. Source: Internet
Graphically, these are the infinite affine hyperplane, the infinite hyper-octant, and the infinite simplex. Source: Internet
For v, w in R 4 introduce the degenerate bilinear form : This degenerate scalar product projects distance measurements in R 4 onto the R 3 hyperplane. Source: Internet
After all, you cannot have the same example on both sides of the separating hyperplane. Source: Internet
The hypercube has eight 3-D hyperfaces (cubes), so that a hyperplane that intersects them all should do so in an octahedron. Source: Internet