Wiktionary
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
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.