The English used in this article or section may not be easy for everybody to understand. (June 2014)
A hyperplane is a space composed of 1 less dimension than the space that it occupies. Visually, a hyperplane in a two-dimensional space (a Cartesian plane) would be a line, which is one-dimensional. A hyperplane in a three-dimensional space would be a plane, or some surface, which is two-dimensional.