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- Contact_(mathematics) abstract "In mathematics, two functions have a contact of order k if, at a point P, they have the same value and k equal derivatives. This is an equivalence relation, whose equivalence classes are generally called jets. The point of osculation is also called the double cusp.One speaks also of curves and geometric objects having k-th order contact at a point: this is also called osculation (i.e. kissing), generalising the property of being tangent. (Here the derivatives are considered with respect to arc length.) An osculating curve from a given family of curves is a curve that has the highest possible order of contact with a given curve at a given point; for instance a tangent line is an osculating curve from the family of lines, and has first-order contact with the given curve; an osculating circle is an osculating curve from the family of circles, and has second-order contact (same tangent angle and curvature), etc.Contact forms are particular differential forms of degree 1 on odd-dimensional manifolds; see contact geometry. Contact transformations are related changes of co-ordinates, of importance in classical mechanics. See also Legendre transformation.Contact between manifolds is often studied in singularity theory, where the type of contact are classified, these include the A series (A0: crossing, A1: tangent, A2: osculating, ...) and the umbilic or D-series where there is a high degree of contact with the sphere.".
- Contact_(mathematics) thumbnail TangentCircle.png?width=300.
- Contact_(mathematics) wikiPageID "396068".
- Contact_(mathematics) wikiPageLength "4881".
- Contact_(mathematics) wikiPageOutDegree "42".
- Contact_(mathematics) wikiPageRevisionID "678645972".
- Contact_(mathematics) wikiPageWikiLink Cambridge_University_Press.
- Contact_(mathematics) wikiPageWikiLink Category:Contact_geometry.
- Contact_(mathematics) wikiPageWikiLink Category:Differential_geometry.
- Contact_(mathematics) wikiPageWikiLink Category:Multivariable_calculus.
- Contact_(mathematics) wikiPageWikiLink Category:Singularity_theory.
- Contact_(mathematics) wikiPageWikiLink Circle.
- Contact_(mathematics) wikiPageWikiLink Classical_mechanics.
- Contact_(mathematics) wikiPageWikiLink Contact_form.
- Contact_(mathematics) wikiPageWikiLink Contact_geometry.
- Contact_(mathematics) wikiPageWikiLink Contact_transformation.
- Contact_(mathematics) wikiPageWikiLink Curvature.
- Contact_(mathematics) wikiPageWikiLink Curve.
- Contact_(mathematics) wikiPageWikiLink Derivative.
- Contact_(mathematics) wikiPageWikiLink Differential_form.
- Contact_(mathematics) wikiPageWikiLink Double_cusp.
- Contact_(mathematics) wikiPageWikiLink Econometrics.
- Contact_(mathematics) wikiPageWikiLink Equivalence_relation.
- Contact_(mathematics) wikiPageWikiLink Evolute.
- Contact_(mathematics) wikiPageWikiLink Four-vertex_theorem.
- Contact_(mathematics) wikiPageWikiLink Function_(mathematics).
- Contact_(mathematics) wikiPageWikiLink Generic.
- Contact_(mathematics) wikiPageWikiLink Ian_R._Porteous.
- Contact_(mathematics) wikiPageWikiLink Inflection_point.
- Contact_(mathematics) wikiPageWikiLink Jet_(mathematics).
- Contact_(mathematics) wikiPageWikiLink Legendre_transformation.
- Contact_(mathematics) wikiPageWikiLink Locus_(mathematics).
- Contact_(mathematics) wikiPageWikiLink Mathematics.
- Contact_(mathematics) wikiPageWikiLink Medial_axis.
- Contact_(mathematics) wikiPageWikiLink Osculating_circle.
- Contact_(mathematics) wikiPageWikiLink Osculating_curve.
- Contact_(mathematics) wikiPageWikiLink Singularity_theory.
- Contact_(mathematics) wikiPageWikiLink Smooth_function.
- Contact_(mathematics) wikiPageWikiLink Smoothness.
- Contact_(mathematics) wikiPageWikiLink Symmetry_set.
- Contact_(mathematics) wikiPageWikiLink Tangent.
- Contact_(mathematics) wikiPageWikiLink Tangent_line.
- Contact_(mathematics) wikiPageWikiLink Umbilic.
- Contact_(mathematics) wikiPageWikiLink Umbilical_point.
- Contact_(mathematics) wikiPageWikiLink Vertex_(curve).
- Contact_(mathematics) wikiPageWikiLink File:OsculatingCircle2.png.
- Contact_(mathematics) wikiPageWikiLink File:TangentCircle.png.
- Contact_(mathematics) wikiPageWikiLink File:VertexOfACurve.png.
- Contact_(mathematics) wikiPageWikiLinkText "4-point contact".
- Contact_(mathematics) wikiPageWikiLinkText "Contact (mathematics)".
- Contact_(mathematics) wikiPageWikiLinkText "contact (mathematics)".
- Contact_(mathematics) wikiPageWikiLinkText "contact element".
- Contact_(mathematics) wikiPageWikiLinkText "contact".
- Contact_(mathematics) wikiPageWikiLinkText "contiguity".
- Contact_(mathematics) hasPhotoCollection Contact_(mathematics).
- Contact_(mathematics) wikiPageUsesTemplate Template:Cite_book.
- Contact_(mathematics) wikiPageUsesTemplate Template:Clarify.
- Contact_(mathematics) wikiPageUsesTemplate Template:Disambiguation_needed.
- Contact_(mathematics) wikiPageUsesTemplate Template:Reflist.
- Contact_(mathematics) subject Category:Contact_geometry.
- Contact_(mathematics) subject Category:Differential_geometry.
- Contact_(mathematics) subject Category:Multivariable_calculus.
- Contact_(mathematics) subject Category:Singularity_theory.
- Contact_(mathematics) comment "In mathematics, two functions have a contact of order k if, at a point P, they have the same value and k equal derivatives. This is an equivalence relation, whose equivalence classes are generally called jets. The point of osculation is also called the double cusp.One speaks also of curves and geometric objects having k-th order contact at a point: this is also called osculation (i.e. kissing), generalising the property of being tangent.".
- Contact_(mathematics) label "Contact (mathematics)".
- Contact_(mathematics) sameAs Berührung_(Mathematik).
- Contact_(mathematics) sameAs Kontakto_(matematiko).
- Contact_(mathematics) sameAs Contact_(géométrie).
- Contact_(mathematics) sameAs Жанасу.
- Contact_(mathematics) sameAs Oskulasjon.
- Contact_(mathematics) sameAs m.0239q5.
- Contact_(mathematics) sameAs Касание.
- Contact_(mathematics) sameAs Dotik_(matematika).
- Contact_(mathematics) sameAs Дотик_(математика).
- Contact_(mathematics) sameAs Q829376.
- Contact_(mathematics) sameAs Q829376.
- Contact_(mathematics) sameAs 切点.
- Contact_(mathematics) wasDerivedFrom Contact_(mathematics)?oldid=678645972.
- Contact_(mathematics) depiction TangentCircle.png.
- Contact_(mathematics) isPrimaryTopicOf Contact_(mathematics).