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Affine plane (incidence geometry) — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-07T17:21:01.790Z
SHA-256 of the archived text: a4cd1f1d518362c01ccaf86260ce3cb272a1913ad57c235f2aadcb0987cde09b
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Affine plane (incidence geometry) — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry) (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_6aaa723b53ea (Metraipolis archive dc_6aaa723b53ea, sha256 a4cd1f1d518362c01ccaf86260ce3cb272a1913ad57c235f2aadcb0987cde09b)

BibTeX

@misc{dc6aaa723b53ea,
  title = {Affine plane (incidence geometry) — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_6aaa723b53ea; sha256 a4cd1f1d518362c01ccaf86260ce3cb272a1913ad57c235f2aadcb0987cde09b},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry). Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In geometry, an affine plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Given any line and any point not on that line there is a unique line which contains the point and does not meet the given line. (Playfair's axiom) There exist four points such that no three are collinear (points not on a single line). In an affine plane, two lines are called parallel if they are equal or disjoint. Using this definition, Playfair's axiom above can be replaced by: Given a point and a line, there is a unique line which contains the point and is parallel to the line. Parallelism is an equivalence relation on the lines of an affine plane. Since no concepts other than those involving the relationship between points and lines are involved in the axioms, an affine plane is an object of study belonging to incidence geometry. They are non-degenerate linear spaces satisfying Playfair's axiom. The familiar Euclidean plane is an affine plane. There are many finite and infinite affine planes. As well as affine planes over fields (and division rings), there are also many non-Desarguesian planes, not derived from coordinates in a division ring, satisfying these axioms. The Moulton plane is an example of one of these.

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «Affine plane (incidence geometry)» — https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)
Wikidata Q382491: «Euclidean space of dimension 2 that is axiomatically defined» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q382491
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Affine_plane_(incidence_geometry)?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1353685649, consultata il 2026-11-07T17:16:50.577Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: de99d158c3f2b11579006ff13790f10373aa2bdc817d7f767039ac3a8b46a4cd