"triangle inequality" meaning in All languages combined

See triangle inequality on Wiktionary

Proper name [English]

Forms: the triangle inequality [canonical]
Head templates: {{en-proper noun|def=1}} the triangle inequality
  1. (mathematical analysis) The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors. Categories (topical): Mathematical analysis
    Sense id: en-triangle_inequality-en-name-fG9XTVs8 Topics: mathematical-analysis, mathematics, sciences
  2. (mathematical analysis) The inequality that states that the distance between two points is less than or equal to the sum of the distances between the first two points and some third point. Categories (topical): Mathematical analysis
    Sense id: en-triangle_inequality-en-name-OSf3x2Tz Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Chinese translations, Terms with Finnish translations, Terms with French translations, Terms with German translations, Terms with Hebrew translations, Terms with Italian translations, Terms with Japanese translations, Terms with Polish translations, Terms with Portuguese translations, Terms with Romanian translations, Terms with Russian translations, Terms with Spanish translations, Terms with Swedish translations Disambiguation of English entries with incorrect language header: 22 49 29 Disambiguation of Entries with translation boxes: 25 51 25 Disambiguation of Pages with 1 entry: 23 51 26 Disambiguation of Pages with entries: 17 58 25 Disambiguation of Terms with Chinese translations: 19 60 20 Disambiguation of Terms with Finnish translations: 23 55 22 Disambiguation of Terms with French translations: 22 58 20 Disambiguation of Terms with German translations: 21 59 20 Disambiguation of Terms with Hebrew translations: 21 59 20 Disambiguation of Terms with Italian translations: 19 60 20 Disambiguation of Terms with Japanese translations: 20 59 21 Disambiguation of Terms with Polish translations: 24 54 21 Disambiguation of Terms with Portuguese translations: 23 53 24 Disambiguation of Terms with Romanian translations: 23 55 22 Disambiguation of Terms with Russian translations: 20 59 21 Disambiguation of Terms with Spanish translations: 17 64 18 Disambiguation of Terms with Swedish translations: 23 54 23 Topics: mathematical-analysis, mathematics, sciences
  3. (mathematical analysis, by abstraction) Either of the above two inequalities, considered as one of the axioms which a function must satisfy to be a norm or metric respectively. Categories (topical): Mathematical analysis
    Sense id: en-triangle_inequality-en-name-zfCx4Ont Topics: mathematical-analysis, mathematics, sciences
The following are not (yet) sense-disambiguated
Translations (the triangle inequality): 三角不等式 (sānjiǎo bùděngshì) (Chinese), kolmioepäyhtälö (Finnish), inégalité triangulaire [feminine] (French), Dreiecksungleichung [feminine] (German), אי שוויון המשולש (Hebrew), disuguaglianza triangolare [feminine] (Italian), 三角不等式 (sankaku futōshiki) (alt: さんかくふとうしき) (Japanese), nierówność trójkąta [feminine] (Polish), desigualdade triangular [feminine] (Portuguese), inegalitatea triunghiului (note: def. form) [feminine] (Romanian), нера́венство треуго́льника (nerávenstvo treugólʹnika) [neuter] (Russian), desigualdad del triángulo [feminine] (Spanish), triangelolikhet [common-gender] (Swedish)
Disambiguation of 'the triangle inequality': 44 44 11
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          "text": "‖ mathbf x+ mathbf y‖≤‖ mathbf x‖+‖ mathbf y‖"
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          "text": "d(x,z)≤d(x,y)+d(y,z)"
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      "code": "zh",
      "lang": "Chinese",
      "roman": "sānjiǎo bùděngshì",
      "sense": "the triangle inequality",
      "word": "三角不等式"
    },
    {
      "_dis1": "44 44 11",
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      "sense": "the triangle inequality",
      "word": "kolmioepäyhtälö"
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      "lang": "French",
      "sense": "the triangle inequality",
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    },
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      "sense": "the triangle inequality",
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      ],
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    },
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      "sense": "the triangle inequality",
      "word": "אי שוויון המשולש"
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      "lang": "Italian",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "disuguaglianza triangolare"
    },
    {
      "_dis1": "44 44 11",
      "alt": "さんかくふとうしき",
      "code": "ja",
      "lang": "Japanese",
      "roman": "sankaku futōshiki",
      "sense": "the triangle inequality",
      "word": "三角不等式"
    },
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      "_dis1": "44 44 11",
      "code": "pl",
      "lang": "Polish",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "nierówność trójkąta"
    },
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      "_dis1": "44 44 11",
      "code": "pt",
      "lang": "Portuguese",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "desigualdade triangular"
    },
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      "code": "ro",
      "lang": "Romanian",
      "note": "def. form",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "inegalitatea triunghiului"
    },
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      "lang": "Russian",
      "roman": "nerávenstvo treugólʹnika",
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      ],
      "word": "нера́венство треуго́льника"
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  "word": "triangle inequality"
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      "lang": "Chinese",
      "roman": "sānjiǎo bùděngshì",
      "sense": "the triangle inequality",
      "word": "三角不等式"
    },
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      "code": "fi",
      "lang": "Finnish",
      "sense": "the triangle inequality",
      "word": "kolmioepäyhtälö"
    },
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      "code": "fr",
      "lang": "French",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "inégalité triangulaire"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "Dreiecksungleichung"
    },
    {
      "code": "he",
      "lang": "Hebrew",
      "sense": "the triangle inequality",
      "word": "אי שוויון המשולש"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "disuguaglianza triangolare"
    },
    {
      "alt": "さんかくふとうしき",
      "code": "ja",
      "lang": "Japanese",
      "roman": "sankaku futōshiki",
      "sense": "the triangle inequality",
      "word": "三角不等式"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "nierówność trójkąta"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "desigualdade triangular"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "note": "def. form",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "inegalitatea triunghiului"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "nerávenstvo treugólʹnika",
      "sense": "the triangle inequality",
      "tags": [
        "neuter"
      ],
      "word": "нера́венство треуго́льника"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "the triangle inequality",
      "tags": [
        "feminine"
      ],
      "word": "desigualdad del triángulo"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "the triangle inequality",
      "tags": [
        "common-gender"
      ],
      "word": "triangelolikhet"
    }
  ],
  "wikipedia": [
    "triangle inequality"
  ],
  "word": "triangle inequality"
}

Download raw JSONL data for triangle inequality meaning in All languages combined (4.8kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-01-18 from the enwiktionary dump dated 2025-01-01 using wiktextract (e4a2c88 and 4230888). 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.