##### Wiktionary

**hyperplane**

n. (context geometry English) 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.)

##### Wikipedia

**Hyperplane**

In geometry a **hyperplane** is a subspace of one dimension less than its ambient space. If a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. This notion can be used in any general space in which the concept of the dimension of a subspace is defined.

In different settings, the objects which are hyperplanes may have different properties. For instance, a hyperplane of an *n*-dimensional affine space is a flat subset with dimension *n* − 1. By its nature, it separates the space into two half spaces. But a hyperplane of an *n*-dimensional projective space does not have this property.

#### Usage examples of "hyperplane".

In a rented __hyperplane__, he and some associates flew home, running an errand for me.

Their little __hyperplane__ was skimming at the brink of space, and the crew was locked inside the cockpit, and the two of them were sharing the little foldout bed.

I followed projecting the n-dimensional __hyperplanes__ into n-1 dimensional spaces, but I got a little tangled up when they started to intersect.

They could approach it through stacks of linear simultaneous equations, each defining parallel __hyperplanes__ in n-dimensional space.