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Get to know Haken better with 7 real example sentences, the meaning.

Rare word

Haken in a sentence

Related words

Haken | Hakenkreuz

Haken meaning

Irreducible, compact, and containing a non-∂-parallel incompressible surface (besides a sphere or disk).

Using Haken

  • The main meaning on this page is: Irreducible, compact, and containing a non-∂-parallel incompressible surface (besides a sphere or disk).
  • In the example corpus, haken often appears in combinations such as: and haken.

Context around Haken

  • Average sentence length in these examples: 24.3 words
  • Position in the sentence: 5 start, 1 middle, 1 end
  • Sentence types: 7 statements, 0 questions, 0 exclamations

Often before:

utilizing 1× appel 1× non 1×

Often after:

concluded 1× proof 1× non 1×

Sentence patterns with Haken

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

appel and haken concluded that 1× appel and haken found an 1× appel and haken were asked 1× by utilizing haken s normal 1× haken and contortionist 1× irreducible non haken non seifert 1× the appel haken proof a 1×

Sentence openings and endings

Common sentence openings:

appel and haken 1× by utilizing haken 1× haken and contortionist 1× in 1986 appel 1× to dispel remaining 1× together with his 1×

Common sentence endings:

1 936 maps 1× as main support 1× could not exist 1× fibered 3 manifolds 1× in their proof 1× seymour and thomas 1×

Words around Haken

Just before it in the word index:

hakeim 2 hakeem 102 hake 32 hakdang 2 hakataramea 2 hakata 5

Just after it in the word index:

hakenkreuz 3 hakes 2 hakham 2 haki 36 hakim 91 hakima 2

Similar in corpus frequency:

aad 10 aadhar 10 aaro 10 abels 10 abidin 10 abidine 10

Corpus analysis for Haken

  • In this selection, "haken" usually appears near the start of the sentence. The average example has 24.3 words, and this corpus slice is mostly made up of statements.
  • Around the word, utilizing, appel, non, concluded, proof and non stand out and add context to how "haken" is used.
  • Recognizable usage signals include appel and haken concluded that and appel and haken found an. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "haken" sits close to words such as aad, aadhar and aaro, which helps place it inside the broader word index.

Example types with haken

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

Haken and Contortionist will alternate as main support. (8 words)

By utilizing Haken 's normal surface techniques, he classified the incompressible surfaces in the knot complement. (16 words)

Appel and Haken concluded that no smallest counterexamples exists because any must contain, yet do not contain, one of these 1,936 maps. (23 words)

Longer example sentences

Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist. (35 words)

Together with his analysis of deformations of hyperbolic structures, he concluded that all but 10 Dehn surgeries on the figure-eight knot resulted in irreducible, non- Haken non- Seifert-fibered 3-manifolds. (32 words)

To dispel remaining doubt about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. (31 words)

Example sentences (7)

Haken and Contortionist will alternate as main support.

Appel and Haken concluded that no smallest counterexamples exists because any must contain, yet do not contain, one of these 1,936 maps.

By utilizing Haken 's normal surface techniques, he classified the incompressible surfaces in the knot complement.

In 1986, Appel and Haken were asked by the editor of Mathematical Intelligencer to write an article addressing the rumors of flaws in their proof.

To dispel remaining doubt about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas.

Together with his analysis of deformations of hyperbolic structures, he concluded that all but 10 Dehn surgeries on the figure-eight knot resulted in irreducible, non- Haken non- Seifert-fibered 3-manifolds.

Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist.

Common combinations with haken

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "haken" in a sentence?
An example: "Haken and Contortionist will alternate as main support." This page contains 7 example sentences with the word "haken" from authentic English texts.
What does "haken" mean?
Haken means: Irreducible, compact, and containing a non-∂-parallel incompressible surface (besides a sphere or disk).
How many example sentences with "haken" are there?
Voorbeeldzinnen.info contains 7 example sentences with "haken", drawn from a database of millions of English sentences.