See continued fraction on Wiktionary
Download JSON data for continued fraction meaning in All languages combined (4.5kB)
{
"forms": [
{
"form": "continued fractions",
"tags": [
"plural"
]
}
],
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{
"args": {},
"expansion": "continued fraction (plural continued fractions)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
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"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "Euler's continued fraction formula"
},
{
"word": "general continued fraction"
},
{
"word": "generalized continued fraction"
},
{
"word": "regular continued fraction"
},
{
"word": "simple continued fraction"
},
{
"word": "periodic continued fraction"
},
{
"word": "finite continued fraction"
},
{
"word": "infinite continued fraction"
},
{
"word": "Rogers-Ramanujan continued fraction"
}
],
"examples": [
{
"ref": "1992, G. E. Andrews, B. C. Berndt, L. Jacobsen, R. L. Lamphere, “The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks”, in Memoirs of the American Mathematical Society, volume 99, number 477, page 1",
"text": "Several results focus on the famous Rogers–Ramanujan continued fraction [47], [48, pp. 214-215], the only continued fraction appearing in Ramanujan's published papers.",
"type": "quotation"
},
{
"text": "2000, Andrew Zardecki, 18: Continued Fractions in Time Series Forec[a]sting, Da Ruan (editor), Fuzzy Systems and Soft Computing in Nuclear Engineering, Physica-Verlag, Studies in Fuzziness and Soft Computing, page 397,\nWe achieve this by using well-known examples from the number theory pertaining to the continued fractions. Any sequence of natural numbers drawn from the probability distribution of the quotients of the continued fraction corresponding to an irrational number represents a typical sequence, in the sense that almost all sequences of quotients have this distribution."
},
{
"ref": "2009, M. Welleda Baldoni, Ciro Ciliberto, G.M. Piacentini Cattaneo, translated by Daniele Gewurz, Elementary Number Theory, Cryptography and Codes, page 48",
"text": "We have seen that all rational numbers, and no other number, can be expressed as finite simple continued fractions.\nThe main reason of interest of continued fractions, however, is in their application to the representation of irrational numbers. To that end we shall need infinite simple continued fractions.",
"type": "quotation"
}
],
"glosses": [
"A compound numerical expression consisting of an integer plus a fraction whose numerator is a positive integer and whose denominator is a continued fraction (an integer plus a fraction), and so on, with finite or infinite recursion."
],
"id": "en-continued_fraction-en-noun-je-YvRmq",
"links": [
[
"mathematics",
"mathematics"
],
[
"number theory",
"number theory"
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[
"expression",
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[
"integer",
"integer"
],
[
"numerator",
"numerator"
],
[
"denominator",
"denominator"
],
[
"finite",
"finite"
],
[
"infinite",
"infinite"
],
[
"recursion",
"recursion"
]
],
"raw_glosses": [
"(mathematics, number theory) A compound numerical expression consisting of an integer plus a fraction whose numerator is a positive integer and whose denominator is a continued fraction (an integer plus a fraction), and so on, with finite or infinite recursion."
],
"related": [
{
"word": "convergent"
}
],
"synonyms": [
{
"tags": [
"attributive"
],
"word": "continued-fraction"
}
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "number theory",
"word": "ketjumurtoluku"
},
{
"code": "fr",
"lang": "French",
"sense": "number theory",
"tags": [
"feminine"
],
"word": "fraction continue"
},
{
"code": "de",
"lang": "German",
"sense": "number theory",
"tags": [
"masculine"
],
"word": "Kettenbruch"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "number theory",
"tags": [
"neuter"
],
"word": "keðjubrot"
},
{
"code": "it",
"lang": "Italian",
"sense": "number theory",
"tags": [
"feminine"
],
"word": "frazione continua"
},
{
"code": "pl",
"lang": "Polish",
"sense": "number theory",
"tags": [
"masculine"
],
"word": "ułamek łańcuchowy"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "number theory",
"tags": [
"neuter"
],
"word": "kedjebråk"
}
],
"wikipedia": [
"continued fraction"
]
}
],
"word": "continued fraction"
}
{
"derived": [
{
"word": "Euler's continued fraction formula"
},
{
"word": "general continued fraction"
},
{
"word": "generalized continued fraction"
},
{
"word": "regular continued fraction"
},
{
"word": "simple continued fraction"
},
{
"word": "periodic continued fraction"
},
{
"word": "finite continued fraction"
},
{
"word": "infinite continued fraction"
},
{
"word": "Rogers-Ramanujan continued fraction"
}
],
"forms": [
{
"form": "continued fractions",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "continued fraction (plural continued fractions)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "convergent"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"en:Mathematics",
"en:Number theory"
],
"examples": [
{
"ref": "1992, G. E. Andrews, B. C. Berndt, L. Jacobsen, R. L. Lamphere, “The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks”, in Memoirs of the American Mathematical Society, volume 99, number 477, page 1",
"text": "Several results focus on the famous Rogers–Ramanujan continued fraction [47], [48, pp. 214-215], the only continued fraction appearing in Ramanujan's published papers.",
"type": "quotation"
},
{
"text": "2000, Andrew Zardecki, 18: Continued Fractions in Time Series Forec[a]sting, Da Ruan (editor), Fuzzy Systems and Soft Computing in Nuclear Engineering, Physica-Verlag, Studies in Fuzziness and Soft Computing, page 397,\nWe achieve this by using well-known examples from the number theory pertaining to the continued fractions. Any sequence of natural numbers drawn from the probability distribution of the quotients of the continued fraction corresponding to an irrational number represents a typical sequence, in the sense that almost all sequences of quotients have this distribution."
},
{
"ref": "2009, M. Welleda Baldoni, Ciro Ciliberto, G.M. Piacentini Cattaneo, translated by Daniele Gewurz, Elementary Number Theory, Cryptography and Codes, page 48",
"text": "We have seen that all rational numbers, and no other number, can be expressed as finite simple continued fractions.\nThe main reason of interest of continued fractions, however, is in their application to the representation of irrational numbers. To that end we shall need infinite simple continued fractions.",
"type": "quotation"
}
],
"glosses": [
"A compound numerical expression consisting of an integer plus a fraction whose numerator is a positive integer and whose denominator is a continued fraction (an integer plus a fraction), and so on, with finite or infinite recursion."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"number theory",
"number theory"
],
[
"expression",
"expression"
],
[
"integer",
"integer"
],
[
"numerator",
"numerator"
],
[
"denominator",
"denominator"
],
[
"finite",
"finite"
],
[
"infinite",
"infinite"
],
[
"recursion",
"recursion"
]
],
"raw_glosses": [
"(mathematics, number theory) A compound numerical expression consisting of an integer plus a fraction whose numerator is a positive integer and whose denominator is a continued fraction (an integer plus a fraction), and so on, with finite or infinite recursion."
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"wikipedia": [
"continued fraction"
]
}
],
"synonyms": [
{
"tags": [
"attributive"
],
"word": "continued-fraction"
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "number theory",
"word": "ketjumurtoluku"
},
{
"code": "fr",
"lang": "French",
"sense": "number theory",
"tags": [
"feminine"
],
"word": "fraction continue"
},
{
"code": "de",
"lang": "German",
"sense": "number theory",
"tags": [
"masculine"
],
"word": "Kettenbruch"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "number theory",
"tags": [
"neuter"
],
"word": "keðjubrot"
},
{
"code": "it",
"lang": "Italian",
"sense": "number theory",
"tags": [
"feminine"
],
"word": "frazione continua"
},
{
"code": "pl",
"lang": "Polish",
"sense": "number theory",
"tags": [
"masculine"
],
"word": "ułamek łańcuchowy"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "number theory",
"tags": [
"neuter"
],
"word": "kedjebråk"
}
],
"word": "continued fraction"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-04 from the enwiktionary dump dated 2024-05-02 using wiktextract (e9e0a99 and db5a844). 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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