hyperplanes's Usage Examples:

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.

geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S.

lines; for generalizations to higher dimensions, see arrangement of hyperplanes.

cosmology is the lowest or densest of a series of planes of existence (hyperplanes that are said to be nested).

regions in n-dimensional Euclidean space by "planks": regions between two hyperplanes.

Most space-partitioning systems use planes (or, in higher dimensions, hyperplanes) to divide space: points on one side of the plane form one region, and.

of non-parallel affine hyperplanes intersect at an affine subspace of dimension n − 2, but a parallel pair of affine hyperplanes intersect at a projective.

of mutually parallel planes; in higher dimensions, they are parallel hyperplanes.

Flats of dimension n − 1 are called hyperplanes.

Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite reflection group.

in n {\displaystyle n} -dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about.

There are many hyperplanes that might classify the data.

buddhic plane (separately, or enclosing and interpenetrating grosser hyperplanes, respectively) or world (simply) in Theosophy is the world in which buddhi.

method for recursively subdividing a space into two convex sets by using hyperplanes as partitions.

The theorem of Bertini states that the set of hyperplanes not containing X and with smooth intersection with X contains an open.

polytope: a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices.

intuition that when a manifold is correctly unfolded, all of the tangent hyperplanes to the manifold will become aligned.

to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.