hyperplane

As a noun hyperplane

is (geometry) 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).

As an adjective undefined is

lacking a definition or value.

As nouns the difference between cabbage and hyperplane

is that cabbage is an edible plant ( ) having a head of green leaves while hyperplane is (geometry) 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).

As a verb cabbage

is to form a head like that of the cabbage.

As nouns the difference between hyperplane and superplane

is that hyperplane is (geometry) 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) while superplane is (informal) a very large or technologically sophisticated aeroplane.

As nouns the difference between hyperplane and horosphere

is that hyperplane is (geometry) 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) while horosphere is an $n-1$-dimensional hyperplane in hyperbolic $n$-dimensional space: it is (in the ) euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) euclidean-parallel to the boundary hyperplane.

In geometry terms the difference between line and hyperplane

is that line is an infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness while hyperplane is 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..

As nouns the difference between line and hyperplane

is that line is a path through two or more points (compare ‘segment’); a continuous mark, including as made by a pen; any path, curved or straight while hyperplane is 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..

As a verb line

is to place (objects) into a line (usually used with "up"); to form into a line; to align.

As nouns the difference between point and hyperplane

is that point is a discrete division of something while hyperplane is (geometry) 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).

As a verb point

is to extend the index finger in the direction of something in order to show where it is or to draw attention to it.

As a proper noun split

is a port city in croatia.

As a noun hyperplane is

(geometry) 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).

As nouns the difference between subspace and hyperplane

is that subspace is (mathematics) a subset of a space which is a space in its own right or subspace can be (bdsm) the psychological state of the submissive or "bottom" during sadomasochistic activity while hyperplane is (geometry) 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).

As nouns the difference between affine and hyperplane

is that affine is a relative by marriage while hyperplane is 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..

As an adjective affine

is assigning finite values to finite quantities.

As a verb affine

is to refine.