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Hyperplane is an English word. Below you'll find 7 example sentences showing how it's used in practice.

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Hyperplane in a sentence

Related words

Hyperplane | Hyperplanes

Hyperplane meaning

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.)

Using Hyperplane

  • The main meaning on this page 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.)
  • In the example corpus, hyperplane often appears in combinations such as: the hyperplane, hyperplane the.

Context around Hyperplane

  • Average sentence length in these examples: 25.4 words
  • Position in the sentence: 2 start, 2 middle, 3 end
  • Sentence types: 7 statements, 0 questions, 0 exclamations

Often before:

dimensional 1× vector 1× affine 1×

Often after:

cuts 1×

Sentence patterns with Hyperplane

These short patterns come directly from the example sentences and show how the word is often embedded:

0 a hyperplane on a 1× a vector hyperplane 1× hyperplane had backed 1× infinite affine hyperplane the infinite 1× leaves the hyperplane 1× r 3 hyperplane 1× three dimensional hyperplane the intersection 1× when the hyperplane cuts right 1×

Sentence openings and endings

Common sentence openings:

a linear subspace 1× graphically these are 1× hyperplane had backed 1× moreover a linear 1×

Common sentence endings:

a vector hyperplane 1× dense or closed 1× leaves the hyperplane 1× r 3 hyperplane 1× shortage in water 1× the 3 sphere 1×

Words around Hyperplane

Just before it in the word index:

hyperpigmentation 21 hyperphosphorylated 3 hyperphosphatemia 2 hyperphenylalaninemia 2 hyperphagia 7 hyperpartisan 8

Just after it in the word index:

hyperplanes 2 hyperplasia 14 hyperplay 2 hyperpnea 3 hyperpolarization 3 hyperpolarized 7

Similar in corpus frequency:

aargau 11 abacos 11 abboud 11 abbreviate 11 abdelkader 11 abdomens 11

Corpus analysis for Hyperplane

  • In this selection, "hyperplane" usually appears near the end of the sentence. The average example has 25.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, dimensional, vector, affine and cuts stand out and add context to how "hyperplane" is used.
  • Recognizable usage signals include 0 a hyperplane on a and a vector hyperplane. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "hyperplane" sits close to words such as aargau, abacos and abboud, which helps place it inside the broader word index.

Example types with hyperplane

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Graphically, these are the infinite affine hyperplane, the infinite hyper-octant, and the infinite simplex. (15 words)

Then the 2-sphere shrinks again down to a single point as the 3-sphere leaves the hyperplane. (18 words)

A linear subspace that contains all elements but one of a basis of the ambient space is a vector hyperplane. (20 words)

Longer example sentences

As a 3-sphere moves through a given three-dimensional hyperplane, the intersection starts out as a point, then becomes a growing 2-sphere that reaches its maximal size when the hyperplane cuts right through the "equator" of the 3-sphere. (41 words)

Moreover, a linear operator f is continuous if f(V) is bounded for some neighborhood V of 0. A hyperplane on a topological vector space X is either dense or closed. (31 words)

Hyperplane had backed a handful of other agtech startups and through that, Myrto discovered that a growing problem for farms will be the increasing shortage in water. (27 words)

Example sentences (7)

As a 3-sphere moves through a given three-dimensional hyperplane, the intersection starts out as a point, then becomes a growing 2-sphere that reaches its maximal size when the hyperplane cuts right through the "equator" of the 3-sphere.

Hyperplane had backed a handful of other agtech startups and through that, Myrto discovered that a growing problem for farms will be the increasing shortage in water.

A linear subspace that contains all elements but one of a basis of the ambient space is a vector hyperplane.

For v, w in R 4 introduce the degenerate bilinear form : This degenerate scalar product projects distance measurements in R 4 onto the R 3 hyperplane.

Graphically, these are the infinite affine hyperplane, the infinite hyper-octant, and the infinite simplex.

Moreover, a linear operator f is continuous if f(V) is bounded for some neighborhood V of 0. A hyperplane on a topological vector space X is either dense or closed.

Then the 2-sphere shrinks again down to a single point as the 3-sphere leaves the hyperplane.

Common combinations with hyperplane

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "hyperplane" in a sentence?
An example: "As a 3-sphere moves through a given three-dimensional hyperplane, the intersection starts out as a point, then becomes a growing 2-sphere that reaches its maximal size when the hyperplane cuts right through the "equator" of the 3-sphere." This page contains 7 example sentences with the word "hyperplane" from authentic English texts.
What does "hyperplane" mean?
Hyperplane means: 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.)
How many example sentences with "hyperplane" are there?
Voorbeeldzinnen.info contains 7 example sentences with "hyperplane", drawn from a database of millions of English sentences.