hyperbolic geometry

collocation in English

meaningsofhyperbolicandgeometry

These words are often used together. Click on the links below to explore the meanings. Or,see other collocations withgeometry.
hyperbolic
adjective
uk
/ˌhaɪ.pəˈbɒl.ɪk/us
/ˌhaɪ.pɚˈbɑː.lɪk/
formal
relating to a way of speaking or writing that makes someone or something sound bigger, better, more, etc., than ...
See more athyperbolic
geometry
noun[U]
uk
/dʒiˈɒm.ə.tri/us
/dʒiˈɑː.mə.tri/
the area of mathematics relating to the study of space and the relationships between points, lines, curves, ...
See more atgeometry

(Definition ofhyperbolicandgeometryfrom theCambridge English Dictionary© Cambridge University Press)

Examplesofhyperbolic geometry

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
This is true by the following elementary arguments fromhyperbolicgeometry.
From theCambridge English Corpus
In complete analogy to the deterministic case, it follows by standard means in the theory ofhyperbolicgeometrythat is relative generator.
From theCambridge English Corpus
It is a fundamental result ofhyperbolicgeometrythat there do not exist triangles of arbitrarily large area.
From theCambridge English Corpus
We assume the known basics onhyperbolicgeometry, continued fractions and dimension groups; however, we have attached an appendix for the reader's benefit.
From theCambridge English Corpus
By their definition, these homeomorphisms have a rigid geometrical structure coming from thehyperbolicgeometryon the universal covering space of the surface.
From theCambridge English Corpus
Briefly, quasiconformal surgery will be the key for the geometrical constructions we do andhyperbolicgeometrywill provide some of the quantitative estimates.
From theCambridge English Corpus
The main reason whyhyperbolicgeometryis very useful in complex dynamics is the fact that all holomorphic maps are contractive, when we look at them under the hyperbolic metric.
From theCambridge English Corpus
The extension tohyperbolicgeometryis slightly problematic because of the multiplicity of parallel (and 'ultraparallel') lines.
From theCambridge English Corpus
Gone is any mention of quaternions orhyperbolicgeometrysince tensor calculus subsumes them.
From
Wikipedia
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More generally, the term "motion" is a synonym for surjective isometry in metric geometry, including elliptic geometry andhyperbolicgeometry.
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Wikipedia
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The development ofhyperbolicgeometrytaught mathematicians that postulates should be regarded as purely formal statements, and not as facts based on experience.
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Wikipedia
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See the entries onhyperbolicgeometryand elliptic geometry for more information.
From
Wikipedia
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The relevant structure is now called the hyperboloid model ofhyperbolicgeometry.
From
Wikipedia
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Hyperbolicgeometryis the most prevalent geometry in this picture and also the most complicated.
From
Wikipedia
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Similarly, the existence of at least one triangle with angle sum of less than 180 degrees implies the characteristic postulate ofhyperbolicgeometry.
From
Wikipedia
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It could, in the absence of dark energy, occur only under a flat orhyperbolicgeometry.
From
Wikipedia
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Hyperbolic space is the principal example of a space exhibitinghyperbolicgeometry.
From
Wikipedia
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He also considered the cases of what are now known as elliptical andhyperbolicgeometry, though he ruled out both of them.
From
Wikipedia
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Focused on low-dimensional topology andhyperbolicgeometry, he is a leading researcher in those subjects.
From
Wikipedia
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These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
Want to learn more?
Go to the definition ofhyperbolic
Go to the definition ofgeometry
See other collocations withgeometry