# Hyperplane

In geometry, a hyperplane is a linear, affine, or projective subspace of codimension 1. In particular, in a three-dimensional space, a hyperplane is the usual plane. In a two-dimensional space, a hyperplane is a line. In a one-dimensional space, a hyperplane is a point.

The true definition is: "A hyperplane is an N-dimensional analogy of a line or plane, which divides an 'N + 1' dimensional space into two." ,from Nature.

An affine hyperplane can be described by a non-degenerate linear equation of the following form:

a1x1 + a2x2 + ... + anxn = b.

A linear hyperplane is similar but with b = 0.

The term realm has been advocated for a three-dimensional hyperplane, but this is not in common use.

A hyperplane is not to be confused with a hypersonic aircraft.de:Hyperebene fr:Hyperplan it:Iperpiano pl:Hiperpłaszczyzna

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