hyperplane

A hyperplane is a generalisation of a geometric plane. A plane in 3D is a flat surface, that is a 2D sheet that, if extended indefinitely, slices the whole 3D space in two. In an N-dimensional space, a hyperplane is N-1 dimensional 'flat surface' that cuts the N-dimensional space in two. It is very hard to think of four, five or higher dimensional spaces, but we can look in the other direction. A line in 2D space is 'flat' 1-dimensional shape that cuts the space in half ... precisely a hyperplane in 2D space.