Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Affine_curvature> ?p ?o. }
Showing items 1 to 30 of
30
with 100 items per page.
- Affine_curvature abstract "This article is about the curvature of affine plane curves, not to be confused with the curvature of an affine connection.Special affine curvature, also known as the equi-affine 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 equi-affine curvature k are precisely all non-singular plane conics. Those with k > 0 are ellipses, those with k = 0 are parabolas, and those with k < 0 are hyperbolas.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 thelimiting position of the (unique) conic through P and four points P1, P2, P3, P4 on the curve, as each of the points approaches 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 (Shirokov 2001b).".
- Affine_curvature wikiPageID "4688641".
- Affine_curvature wikiPageRevisionID "580778193".
- Affine_curvature first "A.P.".
- Affine_curvature hasPhotoCollection Affine_curvature.
- Affine_curvature id "A/a010980".
- Affine_curvature id "a/a010990".
- Affine_curvature last "Shirokov".
- Affine_curvature title "Affine curvature".
- Affine_curvature title "Affine differential geometry".
- Affine_curvature year "2001".
- Affine_curvature subject Category:Affine_geometry.
- Affine_curvature subject Category:Curves.
- Affine_curvature subject Category:Differential_geometry.
- Affine_curvature type Abstraction100002137.
- Affine_curvature type Attribute100024264.
- Affine_curvature type Curve113867641.
- Affine_curvature type Curves.
- Affine_curvature type Line113863771.
- Affine_curvature type Shape100027807.
- Affine_curvature comment "This article is about the curvature of affine plane curves, not to be confused with the curvature of an affine connection.Special affine curvature, also known as the equi-affine 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 equi-affine curvature k are precisely all non-singular plane conics.".
- Affine_curvature label "Affine curvature".
- Affine_curvature label "Аффинная кривизна".
- Affine_curvature label "انحناء أفيني".
- Affine_curvature sameAs m.0chfmy.
- Affine_curvature sameAs Q4072884.
- Affine_curvature sameAs Q4072884.
- Affine_curvature sameAs Affine_curvature.
- Affine_curvature wasDerivedFrom Affine_curvature?oldid=580778193.
- Affine_curvature isPrimaryTopicOf Affine_curvature.