Metraipolis › archive › dc_43ca252adffd

Affine curvature — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Affine_curvature
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-07T17:21:02.896Z
SHA-256 of the archived text: 5c804e699f57fefcadd462bd4e417fe92af10715acc8ef91faadef9acd8c1756
Stable URL of this page: https://metraipolis.com/documento/dc_43ca252adffd

How to cite

Affine curvature — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Affine_curvature (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_43ca252adffd (Metraipolis archive dc_43ca252adffd, sha256 5c804e699f57fefcadd462bd4e417fe92af10715acc8ef91faadef9acd8c1756)

BibTeX

@misc{dc43ca252adffd,
  title = {Affine curvature — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Affine_curvature},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_43ca252adffd; sha256 5c804e699f57fefcadd462bd4e417fe92af10715acc8ef91faadef9acd8c1756},
  year = {2026}
}

Archived text

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

Special affine curvature, also known as the equiaffine curvature or affine curvature, is a particular type of curvature that is defined on a plane curve that remains unchanged under a special affine transformation (an affine transformation that preserves area). The curves of constant equiaffine curvature k are precisely all non-singular plane conics. Those with k > 0 are ellipses, those with k = 0 are parabolae, and those with k < 0 are hyperbolae. The usual Euclidean curvature of a curve at a point is the curvature of its osculating circle, the unique circle making second order contact (having three point contact) with the curve at the point. In the same way, the special affine curvature of a curve at a point P is the special affine curvature of its hyperosculating conic, which is the unique conic making fourth order contact (having five point contact) with the curve at P. In other words, it is the limiting position of the (unique) conic through P and four points P1, P2, P3, P4 on the curve, as each of the points approaches P: P 1 , P 2 , P 3 , P 4 → P . {\displaystyle P_{1},P_{2},P_{3},P_{4}\to P.} In some contexts, the affine curvature refers to a differential invariant κ of the general affine group, which may readily obtained from the special affine curvature k by κ = k−3/2dk/ds, where s is the special affine arc length. Where the general affine group is not used, the special affine curvature k is sometimes also called the affine curvature.

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 curvature» — https://en.wikipedia.org/wiki/Affine_curvature
Wikidata Q4072884 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q4072884
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Affine_curvature?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 1283294982, consultata il 2026-11-07T17:16:50.585Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 4029902e2c7c64fd65260d9f831971095896342cb96505c53c8052b4454a78f8