See Hausdorff dimension on Wiktionary
{
"etymology_text": "Introduced in 1918 by mathematician Felix Hausdorff.",
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"examples": [
{
"text": "If S is nonempty then if the d-dimensional Hausdorff content of S is zero then d is larger than the Hausdorff dimension of S, and if the d-dimensional Hausdorff content of S is infinite then d is smaller or equal to the Hausdorff dimension of S. If the d-dimensional Hausdorff content of S is finite and positive then d is equal to the Hausdorff dimension of S."
}
],
"glosses": [
"A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero."
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"word": "fractal dimension"
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"id": "en-Hausdorff_dimension-en-noun-KAtew0AR",
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"raw_glosses": [
"(mathematical analysis) A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero."
],
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "type of fractal dimension",
"word": "豪斯多夫維數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Háosīduōfū wéishù",
"sense": "type of fractal dimension",
"word": "豪斯多夫维数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "type of fractal dimension",
"word": "Hausdorffova dimenze"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "type of fractal dimension",
"word": "Hausdorffin dimensio"
},
{
"code": "fr",
"lang": "French",
"sense": "type of fractal dimension",
"tags": [
"feminine"
],
"word": "dimension de Hausdorff"
},
{
"code": "el",
"lang": "Greek",
"roman": "diástasi Cháousntorf",
"sense": "type of fractal dimension",
"tags": [
"feminine"
],
"word": "διάσταση Χάουσντορφ"
},
{
"code": "ru",
"lang": "Russian",
"roman": "razmérnostʹ Xausdorfa",
"sense": "type of fractal dimension",
"tags": [
"feminine"
],
"word": "разме́рность Хаусдорфа"
},
{
"code": "es",
"lang": "Spanish",
"sense": "type of fractal dimension",
"tags": [
"feminine"
],
"word": "dimensión de Hausdorff"
}
],
"wikipedia": [
"Felix Hausdorff",
"Hausdorff dimension"
]
}
],
"word": "Hausdorff dimension"
}
{
"etymology_text": "Introduced in 1918 by mathematician Felix Hausdorff.",
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"examples": [
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"text": "If S is nonempty then if the d-dimensional Hausdorff content of S is zero then d is larger than the Hausdorff dimension of S, and if the d-dimensional Hausdorff content of S is infinite then d is smaller or equal to the Hausdorff dimension of S. If the d-dimensional Hausdorff content of S is finite and positive then d is equal to the Hausdorff dimension of S."
}
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"glosses": [
"A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero."
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"raw_glosses": [
"(mathematical analysis) A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero."
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "type of fractal dimension",
"word": "豪斯多夫維數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Háosīduōfū wéishù",
"sense": "type of fractal dimension",
"word": "豪斯多夫维数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "type of fractal dimension",
"word": "Hausdorffova dimenze"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "type of fractal dimension",
"word": "Hausdorffin dimensio"
},
{
"code": "fr",
"lang": "French",
"sense": "type of fractal dimension",
"tags": [
"feminine"
],
"word": "dimension de Hausdorff"
},
{
"code": "el",
"lang": "Greek",
"roman": "diástasi Cháousntorf",
"sense": "type of fractal dimension",
"tags": [
"feminine"
],
"word": "διάσταση Χάουσντορφ"
},
{
"code": "ru",
"lang": "Russian",
"roman": "razmérnostʹ Xausdorfa",
"sense": "type of fractal dimension",
"tags": [
"feminine"
],
"word": "разме́рность Хаусдорфа"
},
{
"code": "es",
"lang": "Spanish",
"sense": "type of fractal dimension",
"tags": [
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],
"word": "dimensión de Hausdorff"
}
],
"word": "Hausdorff dimension"
}
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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