See affine geometry in All languages combined, or Wiktionary
{
"forms": [
{
"form": "affine geometries",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "~"
},
"expansion": "affine geometry (countable and uncountable, plural affine 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"
},
{
"_dis": "76 24",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "63 37",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "75 25",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "79 21",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "67 33",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "66 34",
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "67 33",
"kind": "other",
"name": "Terms with Icelandic translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Russian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "68 32",
"kind": "other",
"name": "Terms with Swedish translations",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"text": "As an alternative to the axiomatic approach, affine geometry can be studied via the properties of affine transformations, which do not, in general, preserve distances or angles, but do preserve alignment of points and parallelism of lines.",
"type": "example"
},
{
"text": "The notion of parallelism remains central to affine geometry, in which the parallel postulate is replaced by Playfair's axiom, a version of the postulate that relies on neither distance nor angle size.",
"type": "example"
},
{
"text": "1940 [McGraw-Hill], E. T. Bell, The Development of Mathematics, 2017 [1992], Dover, page 265,\nTo include affine geometry, Menger (1935) imposed on lattices a reasonable axiom of parallelism."
},
{
"text": "1953 [Addison-Wesley], Dirk J. Struik, Lectures on Analytic and Projective Geometry, 2014, Dover, page 108,\nAnd affine geometry itself can be considered as the geometry of all projective transformations which leave a line invariant."
},
{
"ref": "2005, Miles Reid, Balazs Szendroi, Geometry and Topology, Cambridge University Press, page 62:",
"text": "Affine geometry is the geometry of an n-dimensional vector space together with its inhomogeneous linear structure.[…]Arbitrary affine linear maps take affine linear subspaces into one another, and also preserve collinearity of points, parallels and ratios of distances along parallel lines; all these are thus well defined notions of affine geometry.",
"type": "quote"
}
],
"glosses": [
"The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored."
],
"id": "en-affine_geometry-en-noun-i5qJXM0s",
"links": [
[
"geometry",
"geometry"
],
[
"Euclidean geometry",
"Euclidean geometry"
],
[
"length",
"length"
],
[
"angle",
"angle"
]
],
"raw_glosses": [
"(geometry, uncountable) The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored."
],
"tags": [
"uncountable"
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "61 39",
"code": "fr",
"lang": "French",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "géométrie affine"
},
{
"_dis1": "61 39",
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "affine Geometrie"
},
{
"_dis1": "61 39",
"code": "hu",
"lang": "Hungarian",
"sense": "branch of geometry",
"word": "affin geometria"
},
{
"_dis1": "61 39",
"code": "is",
"lang": "Icelandic",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "vildarrúmfræði"
},
{
"_dis1": "61 39",
"code": "it",
"lang": "Italian",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria affine"
},
{
"_dis1": "61 39",
"code": "ja",
"lang": "Japanese",
"sense": "branch of geometry",
"word": "アフィン幾何学"
},
{
"_dis1": "61 39",
"code": "ru",
"lang": "Russian",
"roman": "affínnaja geométrija",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "аффи́нная геоме́трия"
},
{
"_dis1": "61 39",
"code": "sv",
"lang": "Swedish",
"sense": "branch of geometry",
"tags": [
"common-gender"
],
"word": "affin geometri"
}
]
},
{
"categories": [],
"examples": [
{
"ref": "1989, Walter Prenowitz, Meyer Jordan, Basic Concepts of Geometry, Ardsley House, page 167:",
"text": "This chapter is devoted to the theory of affine geometries: those incidence geometries which satisfy the Euclidean parallel postulate in Playfair's form (Ch. 2, Sec. 2).",
"type": "quote"
},
{
"ref": "1992, James G. Oxley, “Matroid Theory”, in Paperback, Oxford University Press, published 2006, page 178:",
"text": "The affine geometry #123;AG#125;(n,F) is obtained from #123;PG#125;(n,F)^([a projective geometry]) by deleting from the latter all the points of a hyperplane.",
"type": "quote"
},
{
"ref": "2001, W. K. Schief, “An Introduction to Integrable Difference and Differential Geometries”, in Alan Coley et al., editors, Bäcklund and Darboux Transformations: The Geometry of Solitons: AARMS-CRM Workshop, American Mathematical Society, page 69:",
"text": "We here review work on the discretization of affine geometries which was undertaken in collaboration with A. I. Bobenko [7, 8, 37].",
"type": "quote"
}
],
"glosses": [
"A geometry that is otherwise Euclidean but disregards lengths and angle sizes."
],
"id": "en-affine_geometry-en-noun-Chq-ZPNA",
"links": [
[
"Euclidean",
"Euclidean"
]
],
"raw_glosses": [
"(countable) A geometry that is otherwise Euclidean but disregards lengths and angle sizes."
],
"related": [
{
"_dis1": "42 58",
"word": "affine connection"
},
{
"_dis1": "42 58",
"word": "affine group"
},
{
"_dis1": "42 58",
"word": "affine space"
},
{
"_dis1": "42 58",
"word": "affine transformation"
},
{
"_dis1": "42 58",
"word": "centro-affine geometry"
}
],
"tags": [
"countable"
]
}
],
"wikipedia": [
"affine geometry"
],
"word": "affine 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 French translations",
"Terms with German translations",
"Terms with Hungarian translations",
"Terms with Icelandic translations",
"Terms with Italian translations",
"Terms with Japanese translations",
"Terms with Russian translations",
"Terms with Swedish translations"
],
"forms": [
{
"form": "affine geometries",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "~"
},
"expansion": "affine geometry (countable and uncountable, plural affine geometries)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "affine connection"
},
{
"word": "affine group"
},
{
"word": "affine space"
},
{
"word": "affine transformation"
},
{
"word": "centro-affine geometry"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"English terms with usage examples",
"English uncountable nouns",
"en:Geometry"
],
"examples": [
{
"text": "As an alternative to the axiomatic approach, affine geometry can be studied via the properties of affine transformations, which do not, in general, preserve distances or angles, but do preserve alignment of points and parallelism of lines.",
"type": "example"
},
{
"text": "The notion of parallelism remains central to affine geometry, in which the parallel postulate is replaced by Playfair's axiom, a version of the postulate that relies on neither distance nor angle size.",
"type": "example"
},
{
"text": "1940 [McGraw-Hill], E. T. Bell, The Development of Mathematics, 2017 [1992], Dover, page 265,\nTo include affine geometry, Menger (1935) imposed on lattices a reasonable axiom of parallelism."
},
{
"text": "1953 [Addison-Wesley], Dirk J. Struik, Lectures on Analytic and Projective Geometry, 2014, Dover, page 108,\nAnd affine geometry itself can be considered as the geometry of all projective transformations which leave a line invariant."
},
{
"ref": "2005, Miles Reid, Balazs Szendroi, Geometry and Topology, Cambridge University Press, page 62:",
"text": "Affine geometry is the geometry of an n-dimensional vector space together with its inhomogeneous linear structure.[…]Arbitrary affine linear maps take affine linear subspaces into one another, and also preserve collinearity of points, parallels and ratios of distances along parallel lines; all these are thus well defined notions of affine geometry.",
"type": "quote"
}
],
"glosses": [
"The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored."
],
"links": [
[
"geometry",
"geometry"
],
[
"Euclidean geometry",
"Euclidean geometry"
],
[
"length",
"length"
],
[
"angle",
"angle"
]
],
"raw_glosses": [
"(geometry, uncountable) The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored."
],
"tags": [
"uncountable"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
"English countable nouns",
"English terms with quotations"
],
"examples": [
{
"ref": "1989, Walter Prenowitz, Meyer Jordan, Basic Concepts of Geometry, Ardsley House, page 167:",
"text": "This chapter is devoted to the theory of affine geometries: those incidence geometries which satisfy the Euclidean parallel postulate in Playfair's form (Ch. 2, Sec. 2).",
"type": "quote"
},
{
"ref": "1992, James G. Oxley, “Matroid Theory”, in Paperback, Oxford University Press, published 2006, page 178:",
"text": "The affine geometry #123;AG#125;(n,F) is obtained from #123;PG#125;(n,F)^([a projective geometry]) by deleting from the latter all the points of a hyperplane.",
"type": "quote"
},
{
"ref": "2001, W. K. Schief, “An Introduction to Integrable Difference and Differential Geometries”, in Alan Coley et al., editors, Bäcklund and Darboux Transformations: The Geometry of Solitons: AARMS-CRM Workshop, American Mathematical Society, page 69:",
"text": "We here review work on the discretization of affine geometries which was undertaken in collaboration with A. I. Bobenko [7, 8, 37].",
"type": "quote"
}
],
"glosses": [
"A geometry that is otherwise Euclidean but disregards lengths and angle sizes."
],
"links": [
[
"Euclidean",
"Euclidean"
]
],
"raw_glosses": [
"(countable) A geometry that is otherwise Euclidean but disregards lengths and angle sizes."
],
"tags": [
"countable"
]
}
],
"translations": [
{
"code": "fr",
"lang": "French",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "géométrie affine"
},
{
"code": "de",
"lang": "German",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "affine Geometrie"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "branch of geometry",
"word": "affin geometria"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "vildarrúmfræði"
},
{
"code": "it",
"lang": "Italian",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "geometria affine"
},
{
"code": "ja",
"lang": "Japanese",
"sense": "branch of geometry",
"word": "アフィン幾何学"
},
{
"code": "ru",
"lang": "Russian",
"roman": "affínnaja geométrija",
"sense": "branch of geometry",
"tags": [
"feminine"
],
"word": "аффи́нная геоме́трия"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "branch of geometry",
"tags": [
"common-gender"
],
"word": "affin geometri"
}
],
"wikipedia": [
"affine geometry"
],
"word": "affine geometry"
}
Download raw JSONL data for affine geometry meaning in English (5.4kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-01-25 from the enwiktionary dump dated 2025-01-20 using wiktextract (c15a5ce and 5c11237). 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.