See Möbius transformation on Wiktionary
Download JSON data for Möbius transformation meaning in All languages combined (5.0kB)
{
"etymology_text": "Named for German mathematician and theoretical astronomer August Ferdinand Möbius (1790–1868).",
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"name": "Non-Euclidean geometry",
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"examples": [
{
"text": "2008, J. Vernon Armitage, John Parker, Jørgensen's inequality for Non-Archimedean Metric Spaces, Mikhail Kapranov, Sergii Kolyada, Yu. I. Manin, Pieter Moree, Leonid Potyagailo (editors), Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov, page 97,\nJørgensen's inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete."
},
{
"text": "2012, Martin Delacourt, Petr Kůrka, Finite State Transducers of Modular Möbius Number Systems, Branislav Rovan, Vladimiro Sassone, Peter Widmayer (editors), Mathematical Foundations of Computer Science 2012, 37th International Symposium, MFCS 2012, Proceedings, Springer, LNCS 7464, page 323,\nModular Möbius number systems consist of Möbius transformations with integer coefficients and unit determinant."
},
{
"ref": "2013, Angel Cano, Juan Pablo Navarrete, Seade Kuri José Antonio, Complex Kleinian Groups, page 1",
"text": "Classical Kleinian groups are discrete subgroups of Möbius transformations which act on the Riemann sphere with a nonempty region of discontinuity.",
"type": "quotation"
}
],
"glosses": [
"A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line."
],
"holonyms": [
{
"word": "Möbius group"
}
],
"hypernyms": [
{
"word": "automorphism"
},
{
"word": "conformal mapping"
},
{
"sense": "linear fractional transformation",
"word": "homography"
},
{
"sense": "linear fractional transformation",
"word": "projective transformation"
}
],
"id": "en-Möbius_transformation-en-noun-PN1hJSoo",
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"complex projective line",
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],
"raw_glosses": [
"(geometry, complex analysis) A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line."
],
"synonyms": [
{
"word": "Mobius transformation"
},
{
"word": "Moebius transformation"
}
],
"topics": [
"complex-analysis",
"geometry",
"mathematics",
"sciences"
],
"translations": [
{
"code": "nl",
"lang": "Dutch",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "Möbius-transformatie"
},
{
"code": "fr",
"lang": "French",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "transformation de Möbius"
},
{
"code": "de",
"lang": "German",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "Möbiustransformation"
},
{
"code": "it",
"lang": "Italian",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "trasformazione di Möbius"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "transformação de Möbius"
},
{
"code": "es",
"lang": "Spanish",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "transformación de Möbius"
}
],
"wikipedia": [
"August Ferdinand Möbius",
"Möbius transformation"
]
}
],
"word": "Möbius transformation"
}
{
"etymology_text": "Named for German mathematician and theoretical astronomer August Ferdinand Möbius (1790–1868).",
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"word": "projective transformation"
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"text": "2008, J. Vernon Armitage, John Parker, Jørgensen's inequality for Non-Archimedean Metric Spaces, Mikhail Kapranov, Sergii Kolyada, Yu. I. Manin, Pieter Moree, Leonid Potyagailo (editors), Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov, page 97,\nJørgensen's inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete."
},
{
"text": "2012, Martin Delacourt, Petr Kůrka, Finite State Transducers of Modular Möbius Number Systems, Branislav Rovan, Vladimiro Sassone, Peter Widmayer (editors), Mathematical Foundations of Computer Science 2012, 37th International Symposium, MFCS 2012, Proceedings, Springer, LNCS 7464, page 323,\nModular Möbius number systems consist of Möbius transformations with integer coefficients and unit determinant."
},
{
"ref": "2013, Angel Cano, Juan Pablo Navarrete, Seade Kuri José Antonio, Complex Kleinian Groups, page 1",
"text": "Classical Kleinian groups are discrete subgroups of Möbius transformations which act on the Riemann sphere with a nonempty region of discontinuity.",
"type": "quotation"
}
],
"glosses": [
"A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line."
],
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"raw_glosses": [
"(geometry, complex analysis) A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line."
],
"topics": [
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"Möbius transformation"
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"synonyms": [
{
"word": "Mobius transformation"
},
{
"word": "Moebius transformation"
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"translations": [
{
"code": "nl",
"lang": "Dutch",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "Möbius-transformatie"
},
{
"code": "fr",
"lang": "French",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "transformation de Möbius"
},
{
"code": "de",
"lang": "German",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "Möbiustransformation"
},
{
"code": "it",
"lang": "Italian",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "trasformazione di Möbius"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "transformação de Möbius"
},
{
"code": "es",
"lang": "Spanish",
"sense": "transformation of the complex plane",
"tags": [
"feminine"
],
"word": "transformación de Möbius"
}
],
"word": "Möbius transformation"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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