See Egyptian fraction on Wiktionary
Download JSON data for Egyptian fraction meaning in All languages combined (3.9kB)
{
"forms": [
{
"form": "Egyptian fractions",
"tags": [
"plural"
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"head_templates": [
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"args": {},
"expansion": "Egyptian fraction (plural Egyptian fractions)",
"name": "en-noun"
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"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"text": "The fraction #x5C;frac#x7B;7#x7D;#x7B;10#x7D; can be written as the Egyptian fraction #x5C;frac#x7B;1#x7D;#x7B;2#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;5#x7D;.",
"type": "example"
},
{
"text": "The calculation of Mᴺ where both M and N are real numbers can be done by expressing N as the sum of an integer h and an Egyptian fraction 1#x2F;g#x5F;1#x2B;1#x2F;g#x5F;2#x2B;1#x2F;g#x5F;3#x2B;.... Then Mᴺ#x3D;Mʰ#x5C;sqrt#x5B;g#x5F;1#x5D;#x7B;M#x7D;#x5C;sqrt#x5B;g#x5F;2#x5D;#x7B;M#x7D;#x5C;sqrt#x5B;g#x5F;3#x5D;#x7B;M#x7D;... where each of the roots can be calculated by means of the Newton–Raphson method.",
"type": "example"
},
{
"text": "1995, C. Pomerance, A. Sárkőzy, Combinatorial number theory, R. L. Graham, M. Grötschel, L. Lovász (edtors), Handbook of Combinatorics, Elsevier (North-Holland), page 1014,\nHowever, a representation of r as a sum of distinct Egyptian fractions is certainly not unique and this fact leads to many questions."
},
{
"ref": "2013, R. L. Graham, “Paul Erdős and Egyptian Fractions”, in László Lovász, Imre Ruzsa, Vera T. Sós, editors, Erdős Centennial, Springer,, page 293",
"text": "In [27], Erdős also considers various questions relating to Egyptian fraction decompositions of #x5C;textstyle 1#x3D;#x5C;sumⁿ#x5F;#x7B;k#x3D;1#x7D;#x5C;frac#x7B;1#x7D;#x7B;x#x5F;k#x7D;.",
"type": "quotation"
},
{
"ref": "2016, Annette Imhausen, Mathematics in Ancient Egypt: A Contextual History, Princeton University Press, page 5",
"text": "The modern description of Egyptian fraction reckoning being \"restricted\" to unit fractions is obviously anachronistic (indeed, the Egyptian concept of fractions did not include a numerator, but from a historian's point of view this cannot be criticized on the basis that our modern fractions consist of denominator and numerator). Furthermore, this criticism does not do justice to the development of Egyptian fractions.",
"type": "quotation"
}
],
"glosses": [
"A representation of a rational number as a sum of distinct unit fractions."
],
"id": "en-Egyptian_fraction-en-noun-YMCi-eCo",
"links": [
[
"number theory",
"number theory"
],
[
"unit fraction",
"unit fraction"
]
],
"raw_glosses": [
"(number theory) A representation of a rational number as a sum of distinct unit fractions."
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"_dis1": "69 31",
"code": "fi",
"lang": "Finnish",
"sense": "representation of a rational number as sum of distinct unit fractions",
"word": "egyptiläinen murtoluku"
}
]
},
{
"categories": [
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"kind": "topical",
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"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "35 65",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
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"Entry maintenance"
],
"source": "w+disamb"
}
],
"glosses": [
"A unit fraction."
],
"id": "en-Egyptian_fraction-en-noun-FNFtyCOa",
"links": [
[
"number theory",
"number theory"
],
[
"unit fraction",
"unit fraction"
]
],
"raw_glosses": [
"(number theory, rare) A unit fraction."
],
"tags": [
"rare"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"_dis1": "29 71",
"code": "fi",
"lang": "Finnish",
"sense": "unit fraction",
"word": "yksikkömurtoluku"
},
{
"_dis1": "29 71",
"code": "mi",
"lang": "Maori",
"sense": "unit fraction",
"word": "hautau waetahi"
}
]
}
],
"wikipedia": [
"Egyptian fraction"
],
"word": "Egyptian fraction"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns"
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"forms": [
{
"form": "Egyptian fractions",
"tags": [
"plural"
]
}
],
"head_templates": [
{
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"expansion": "Egyptian fraction (plural Egyptian fractions)",
"name": "en-noun"
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"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
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"English terms with usage examples",
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"examples": [
{
"text": "The fraction #x5C;frac#x7B;7#x7D;#x7B;10#x7D; can be written as the Egyptian fraction #x5C;frac#x7B;1#x7D;#x7B;2#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;5#x7D;.",
"type": "example"
},
{
"text": "The calculation of Mᴺ where both M and N are real numbers can be done by expressing N as the sum of an integer h and an Egyptian fraction 1#x2F;g#x5F;1#x2B;1#x2F;g#x5F;2#x2B;1#x2F;g#x5F;3#x2B;.... Then Mᴺ#x3D;Mʰ#x5C;sqrt#x5B;g#x5F;1#x5D;#x7B;M#x7D;#x5C;sqrt#x5B;g#x5F;2#x5D;#x7B;M#x7D;#x5C;sqrt#x5B;g#x5F;3#x5D;#x7B;M#x7D;... where each of the roots can be calculated by means of the Newton–Raphson method.",
"type": "example"
},
{
"text": "1995, C. Pomerance, A. Sárkőzy, Combinatorial number theory, R. L. Graham, M. Grötschel, L. Lovász (edtors), Handbook of Combinatorics, Elsevier (North-Holland), page 1014,\nHowever, a representation of r as a sum of distinct Egyptian fractions is certainly not unique and this fact leads to many questions."
},
{
"ref": "2013, R. L. Graham, “Paul Erdős and Egyptian Fractions”, in László Lovász, Imre Ruzsa, Vera T. Sós, editors, Erdős Centennial, Springer,, page 293",
"text": "In [27], Erdős also considers various questions relating to Egyptian fraction decompositions of #x5C;textstyle 1#x3D;#x5C;sumⁿ#x5F;#x7B;k#x3D;1#x7D;#x5C;frac#x7B;1#x7D;#x7B;x#x5F;k#x7D;.",
"type": "quotation"
},
{
"ref": "2016, Annette Imhausen, Mathematics in Ancient Egypt: A Contextual History, Princeton University Press, page 5",
"text": "The modern description of Egyptian fraction reckoning being \"restricted\" to unit fractions is obviously anachronistic (indeed, the Egyptian concept of fractions did not include a numerator, but from a historian's point of view this cannot be criticized on the basis that our modern fractions consist of denominator and numerator). Furthermore, this criticism does not do justice to the development of Egyptian fractions.",
"type": "quotation"
}
],
"glosses": [
"A representation of a rational number as a sum of distinct unit fractions."
],
"links": [
[
"number theory",
"number theory"
],
[
"unit fraction",
"unit fraction"
]
],
"raw_glosses": [
"(number theory) A representation of a rational number as a sum of distinct unit fractions."
],
"topics": [
"mathematics",
"number-theory",
"sciences"
]
},
{
"categories": [
"English terms with rare senses",
"en:Number theory"
],
"glosses": [
"A unit fraction."
],
"links": [
[
"number theory",
"number theory"
],
[
"unit fraction",
"unit fraction"
]
],
"raw_glosses": [
"(number theory, rare) A unit fraction."
],
"tags": [
"rare"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
]
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "representation of a rational number as sum of distinct unit fractions",
"word": "egyptiläinen murtoluku"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "unit fraction",
"word": "yksikkömurtoluku"
},
{
"code": "mi",
"lang": "Maori",
"sense": "unit fraction",
"word": "hautau waetahi"
}
],
"wikipedia": [
"Egyptian fraction"
],
"word": "Egyptian 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 2024-05-15 from the enwiktionary dump dated 2024-05-02 using wiktextract (8203a16 and 304864d). 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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