See continued fraction in All languages combined, or Wiktionary
{ "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", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Mandarin terms with redundant transliterations", "parents": [ "Terms with redundant transliterations", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Icelandic translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Korean translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Mandarin translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w" }, { "kind": "other", "langcode": "en", "name": "Infinity", "orig": "en:Infinity", "parents": [], "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": "finite continued fraction" }, { "word": "general continued fraction" }, { "word": "generalized continued fraction" }, { "word": "infinite continued fraction" }, { "word": "periodic continued fraction" }, { "word": "regular continued fraction" }, { "word": "Rogers-Ramanujan continued fraction" }, { "word": "simple 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": "quote" }, { "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": "quote" } ], "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" ], [ "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." ], "related": [ { "word": "convergent" } ], "synonyms": [ { "tags": [ "attributive" ], "word": "continued-fraction" } ], "topics": [ "mathematics", "number-theory", "sciences" ], "translations": [ { "code": "cmn", "lang": "Chinese Mandarin", "roman": "liánfēnshù", "sense": "number theory", "word": "連分數 /连分数" }, { "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": "ko", "lang": "Korean", "roman": "yeonbunsu", "sense": "number theory", "word": "연분수" }, { "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": "finite continued fraction" }, { "word": "general continued fraction" }, { "word": "generalized continued fraction" }, { "word": "infinite continued fraction" }, { "word": "periodic continued fraction" }, { "word": "regular continued fraction" }, { "word": "Rogers-Ramanujan continued fraction" }, { "word": "simple 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", "Entries with translation boxes", "Mandarin terms with redundant transliterations", "Pages with 1 entry", "Pages with entries", "Terms with Finnish translations", "Terms with French translations", "Terms with German translations", "Terms with Icelandic translations", "Terms with Italian translations", "Terms with Korean translations", "Terms with Mandarin translations", "Terms with Polish translations", "Terms with Swedish translations", "en:Infinity", "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": "quote" }, { "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": "quote" } ], "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": "cmn", "lang": "Chinese Mandarin", "roman": "liánfēnshù", "sense": "number theory", "word": "連分數 /连分数" }, { "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": "ko", "lang": "Korean", "roman": "yeonbunsu", "sense": "number theory", "word": "연분수" }, { "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" }
Download raw JSONL data for continued fraction meaning in English (4.8kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-01-25 from the enwiktionary dump dated 2025-01-20 using wiktextract (c15a5ce and 5c11237). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.