"Minkowski-Bouligand dimension" meaning in English

See Minkowski-Bouligand dimension in All languages combined, or Wiktionary

Noun

Forms: Minkowski-Bouligand dimensions [plural]
Etymology: Named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand. Head templates: {{en-noun}} Minkowski-Bouligand dimension (plural Minkowski-Bouligand dimensions)
  1. (geometry) A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by imagining the fractal lying on an evenly-spaced grid and counting how many boxes are required to cover the set. The dimension is then calculated by seeing how this number changes as the grid is made finer. Categories (topical): Geometry Synonyms: box-counting dimension, Minkowski dimension

Inflected forms

{
  "etymology_text": "Named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand.",
  "forms": [
    {
      "form": "Minkowski-Bouligand dimensions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Minkowski-Bouligand dimension (plural Minkowski-Bouligand dimensions)",
      "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": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by imagining the fractal lying on an evenly-spaced grid and counting how many boxes are required to cover the set. The dimension is then calculated by seeing how this number changes as the grid is made finer."
      ],
      "id": "en-Minkowski-Bouligand_dimension-en-noun-6e2FMs86",
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "fractal dimension",
          "fractal dimension"
        ],
        [
          "set",
          "set"
        ],
        [
          "Euclidean space",
          "Euclidean space"
        ],
        [
          "metric space",
          "metric space"
        ]
      ],
      "raw_glosses": [
        "(geometry) A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by imagining the fractal lying on an evenly-spaced grid and counting how many boxes are required to cover the set. The dimension is then calculated by seeing how this number changes as the grid is made finer."
      ],
      "synonyms": [
        {
          "word": "box-counting dimension"
        },
        {
          "word": "Minkowski dimension"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Minkowski-Bouligand dimension"
}
{
  "etymology_text": "Named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand.",
  "forms": [
    {
      "form": "Minkowski-Bouligand dimensions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Minkowski-Bouligand dimension (plural Minkowski-Bouligand dimensions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "Pages with 1 entry",
        "en:Geometry"
      ],
      "glosses": [
        "A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by imagining the fractal lying on an evenly-spaced grid and counting how many boxes are required to cover the set. The dimension is then calculated by seeing how this number changes as the grid is made finer."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "fractal dimension",
          "fractal dimension"
        ],
        [
          "set",
          "set"
        ],
        [
          "Euclidean space",
          "Euclidean space"
        ],
        [
          "metric space",
          "metric space"
        ]
      ],
      "raw_glosses": [
        "(geometry) A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by imagining the fractal lying on an evenly-spaced grid and counting how many boxes are required to cover the set. The dimension is then calculated by seeing how this number changes as the grid is made finer."
      ],
      "synonyms": [
        {
          "word": "box-counting dimension"
        },
        {
          "word": "Minkowski dimension"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Minkowski-Bouligand dimension"
}

Download raw JSONL data for Minkowski-Bouligand dimension meaning in English (1.8kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-09-22 from the enwiktionary dump dated 2024-09-20 using wiktextract (af5c55c and 66545a6). 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.