See spherical geometry in All languages combined, or Wiktionary
{
"forms": [
{
"form": "spherical geometries",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "-",
"2": "+"
},
"expansion": "spherical geometry (usually uncountable, plural spherical geometries)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"text": "The basic concepts of Euclidean geometry of the plane are the point and the (straight) line; in spherical geometry, the corresponding concepts are the point and the great circle.",
"type": "example"
},
{
"text": "Due to the way the geometry of a sphere's surface differs from that of the plane, spherical geometry has some features of a non-Euclidean geometry and is sometimes described as being one. Historically, however, spherical geometry was not considered a fully fledged (non-Euclidean) geometry capable of resolving the question of whether the parallel postulate is a logical consequence of the rest of Euclid's axioms of plane geometry.",
"type": "example"
},
{
"text": "1972, Morris Kline, Mathematical Thought from Ancient to Modern Times: Volume 1, Oxford University Press, 1990, paperback, page 119,\nSpherical trigonometry presupposes spherical geometry, for example the properties of great circles and spherical triangles, much of which was already known; it had been investigated as soon as astronomy became mathematical, during the time of the later Pythagoreans."
},
{
"ref": "1994, Viacheslav V. Nikulin, Igor R. Shafarevich, translated by Miles Reid, Geometries and Groups, Springer, page 194:",
"text": "We start with spherical geometries. The two geometries on spheres of radiuses R₁ and R₂ are obviously identical if R₁ = R₂; moreover, the converse also holds.",
"type": "quote"
},
{
"ref": "2008, Sherif Ghali, Introduction to Geometric Computing, Springer, page 272:",
"text": "To collect the boundary of the point set in the tree we pass a bounding box (for Euclidean geometries) or the universal set (for spherical geometries) to the root of the tree.",
"type": "quote"
},
{
"text": "2020, Marshall A. Whittlesey, Spherical Geometry and Its Applications, Taylor & Francis (CRC Press), unnumbered page,\nIt has been at least fifty years since spherical geometry and spherical trigonometry have been a regular part of the high school or undergraduate curriculum."
}
],
"glosses": [
"The geometry of the 2-dimensional surface of a sphere;"
],
"id": "en-spherical_geometry-en-noun-JaO0BJ3L",
"links": [
[
"geometry",
"geometry"
],
[
"2-dimensional",
"2-dimensional"
],
[
"sphere",
"sphere"
]
],
"raw_glosses": [
"(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;"
],
"tags": [
"uncountable",
"usually"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "40 60",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "21 79",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "34 66",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "29 71",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "22 78",
"kind": "other",
"name": "Terms with Catalan translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "21 79",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "22 78",
"kind": "other",
"name": "Terms with Georgian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "22 78",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "25 75",
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "21 79",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "21 79",
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "25 75",
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "22 78",
"kind": "other",
"name": "Terms with Romanian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "18 82",
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "22 78",
"kind": "other",
"name": "Terms with Tagalog translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "33 67",
"kind": "other",
"langcode": "en",
"name": "Non-Euclidean geometry",
"orig": "en:Non-Euclidean geometry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "44 56",
"kind": "other",
"langcode": "en",
"name": "Sphere",
"orig": "en:Sphere",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"The geometry of the 2-dimensional surface of a sphere;\n(countable) a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres.",
"a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres."
],
"id": "en-spherical_geometry-en-noun-wRQLL4Hg",
"links": [
[
"geometry",
"geometry"
],
[
"2-dimensional",
"2-dimensional"
],
[
"sphere",
"sphere"
]
],
"raw_glosses": [
"(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;"
],
"related": [
{
"_dis1": "42 58",
"word": "spherical trigonometry"
},
{
"_dis1": "42 58",
"word": "astrometry"
},
{
"_dis1": "42 58",
"word": "elliptic geometry"
},
{
"_dis1": "42 58",
"word": "great circle"
},
{
"_dis1": "42 58",
"word": "non-Euclidean geometry"
},
{
"_dis1": "42 58",
"word": "parallel postulate"
}
],
"tags": [
"countable",
"usually"
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "42 58",
"code": "ca",
"lang": "Catalan",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria esfèrica"
},
{
"_dis1": "42 58",
"code": "fr",
"lang": "French",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "géométrie sphérique"
},
{
"_dis1": "42 58",
"code": "ka",
"lang": "Georgian",
"roman": "speruli geomeṭria",
"sense": "branch of geometry",
"word": "სფერული გეომეტრია"
},
{
"_dis1": "42 58",
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "sphärische Geometrie"
},
{
"_dis1": "42 58",
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "Kugelgeometrie"
},
{
"_dis1": "42 58",
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "Geometrie auf der Kugel"
},
{
"_dis1": "42 58",
"code": "hu",
"lang": "Hungarian",
"sense": "branch of geometry",
"word": "gömbi geometria"
},
{
"_dis1": "42 58",
"code": "it",
"lang": "Italian",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria sferica"
},
{
"_dis1": "42 58",
"code": "ja",
"lang": "Japanese",
"sense": "branch of geometry",
"word": "球面幾何学"
},
{
"_dis1": "42 58",
"code": "pt",
"lang": "Portuguese",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria esférica"
},
{
"_dis1": "42 58",
"code": "ro",
"lang": "Romanian",
"sense": "branch of geometry",
"word": "geometrie sferică"
},
{
"_dis1": "42 58",
"code": "es",
"lang": "Spanish",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometría esférica"
},
{
"_dis1": "42 58",
"code": "tl",
"lang": "Tagalog",
"sense": "branch of geometry",
"word": "timbuluging sukgisan"
}
]
}
],
"wikipedia": [
"spherical geometry"
],
"word": "spherical geometry"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English uncountable nouns",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Catalan translations",
"Terms with French translations",
"Terms with Georgian translations",
"Terms with German translations",
"Terms with Hungarian translations",
"Terms with Italian translations",
"Terms with Japanese translations",
"Terms with Portuguese translations",
"Terms with Romanian translations",
"Terms with Spanish translations",
"Terms with Tagalog translations",
"en:Non-Euclidean geometry",
"en:Sphere"
],
"forms": [
{
"form": "spherical geometries",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "-",
"2": "+"
},
"expansion": "spherical geometry (usually uncountable, plural spherical geometries)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "spherical trigonometry"
},
{
"word": "astrometry"
},
{
"word": "elliptic geometry"
},
{
"word": "great circle"
},
{
"word": "non-Euclidean geometry"
},
{
"word": "parallel postulate"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English terms with quotations",
"English terms with usage examples",
"English uncountable nouns",
"en:Geometry"
],
"examples": [
{
"text": "The basic concepts of Euclidean geometry of the plane are the point and the (straight) line; in spherical geometry, the corresponding concepts are the point and the great circle.",
"type": "example"
},
{
"text": "Due to the way the geometry of a sphere's surface differs from that of the plane, spherical geometry has some features of a non-Euclidean geometry and is sometimes described as being one. Historically, however, spherical geometry was not considered a fully fledged (non-Euclidean) geometry capable of resolving the question of whether the parallel postulate is a logical consequence of the rest of Euclid's axioms of plane geometry.",
"type": "example"
},
{
"text": "1972, Morris Kline, Mathematical Thought from Ancient to Modern Times: Volume 1, Oxford University Press, 1990, paperback, page 119,\nSpherical trigonometry presupposes spherical geometry, for example the properties of great circles and spherical triangles, much of which was already known; it had been investigated as soon as astronomy became mathematical, during the time of the later Pythagoreans."
},
{
"ref": "1994, Viacheslav V. Nikulin, Igor R. Shafarevich, translated by Miles Reid, Geometries and Groups, Springer, page 194:",
"text": "We start with spherical geometries. The two geometries on spheres of radiuses R₁ and R₂ are obviously identical if R₁ = R₂; moreover, the converse also holds.",
"type": "quote"
},
{
"ref": "2008, Sherif Ghali, Introduction to Geometric Computing, Springer, page 272:",
"text": "To collect the boundary of the point set in the tree we pass a bounding box (for Euclidean geometries) or the universal set (for spherical geometries) to the root of the tree.",
"type": "quote"
},
{
"text": "2020, Marshall A. Whittlesey, Spherical Geometry and Its Applications, Taylor & Francis (CRC Press), unnumbered page,\nIt has been at least fifty years since spherical geometry and spherical trigonometry have been a regular part of the high school or undergraduate curriculum."
}
],
"glosses": [
"The geometry of the 2-dimensional surface of a sphere;"
],
"links": [
[
"geometry",
"geometry"
],
[
"2-dimensional",
"2-dimensional"
],
[
"sphere",
"sphere"
]
],
"raw_glosses": [
"(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;"
],
"tags": [
"uncountable",
"usually"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
"English countable nouns",
"English terms with quotations",
"English terms with usage examples",
"English uncountable nouns",
"en:Geometry"
],
"glosses": [
"The geometry of the 2-dimensional surface of a sphere;\n(countable) a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres.",
"a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres."
],
"links": [
[
"geometry",
"geometry"
],
[
"2-dimensional",
"2-dimensional"
],
[
"sphere",
"sphere"
]
],
"raw_glosses": [
"(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;"
],
"tags": [
"countable",
"usually"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
}
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria esfèrica"
},
{
"code": "fr",
"lang": "French",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "géométrie sphérique"
},
{
"code": "ka",
"lang": "Georgian",
"roman": "speruli geomeṭria",
"sense": "branch of geometry",
"word": "სფერული გეომეტრია"
},
{
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "sphärische Geometrie"
},
{
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "Kugelgeometrie"
},
{
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "Geometrie auf der Kugel"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "branch of geometry",
"word": "gömbi geometria"
},
{
"code": "it",
"lang": "Italian",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria sferica"
},
{
"code": "ja",
"lang": "Japanese",
"sense": "branch of geometry",
"word": "球面幾何学"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria esférica"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "branch of geometry",
"word": "geometrie sferică"
},
{
"code": "es",
"lang": "Spanish",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometría esférica"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "branch of geometry",
"word": "timbuluging sukgisan"
}
],
"wikipedia": [
"spherical geometry"
],
"word": "spherical geometry"
}
Download raw JSONL data for spherical geometry meaning in English (5.9kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.