Osculating plane

A space curve, Frenet–Serret frame, and the osculating plane (spanned by T and N).

In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point. The word osculate is from the Latin osculatus which is a past participle of osculari, meaning to kiss. An osculating plane is thus a plane which "kisses" a submanifold.

The osculating plane in the geometry of Euclidean space curves can be described in terms of the Frenet-Serret formulas as the linear span of the tangent and normal vectors. See also Differential geometry of curves#Special Frenet vectors and generalized curvatures.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometry stubs Differential geometry Wikimedia Foundation. 2010. Игры ⚽ Поможем решить контрольную работу Ray Handley Rod Rust Look at other dictionaries: osculating plane — Math. the plane containing the circle of curvature of a point on a given curve. [1860 65] * * * …   Universalium osculating plane — Math. the plane containing the circle of curvature of a point on a given curve. [1860 65] …   Useful english dictionary Osculating circle — Kissing circles redirects here. For Descartes theorem on mutually tangent (kissing) circles, see Descartes theorem. An osculating circle In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given… …   Wikipedia Osculating circle of a curve — Circle Cir cle (s[ e]r k l), n. [OE. cercle, F. cercle, fr. L. circulus (Whence also AS. circul), dim. of circus circle, akin to Gr. kri kos, ki rkos, circle, ring. Cf. {Circus}, {Circum }.] [1913 Webster] 1. A plane figure, bounded by a single… …   The Collaborative International Dictionary of English osculating circle — noun the circle that touches a curve (on the concave side) and whose radius is the radius of curvature • Syn: ↑circle of curvature • Hypernyms: ↑circle * * * noun : a circle which is tangent to a curve at a given point, which lies in the limiting …   Useful english dictionary Osculatory plane — Osculatory Os cu*la*to*ry, a. 1. Of or pertaining to kissing; kissing. The osculatory ceremony. Thackeray. [1913 Webster] 2. (Geom.) Pertaining to, or having the properties of, an osculatrix; capable of osculation; as, a circle may be osculatory… …   The Collaborative International Dictionary of English Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia Differential geometry of curves — This article considers only curves in Euclidean space. Most of the notions presented here have analogues for curves in Riemannian and pseudo Riemannian manifolds. For a discussion of curves in an arbitrary topological space, see the main article… …   Wikipedia Repère de Frenet — En cinématique ou en géométrie différentielle, le repère de Frenet ou repère de Serret Frenet est un outil d étude du comportement local des courbes. Il s agit d un repère local associé à un point P, décrivant une courbe (C). Son mode de… …   Wikipédia en Français List of mathematics articles (O) — NOTOC O O minimal theory O Nan group O(n) Obelus Oberwolfach Prize Object of the mind Object theory Oblate spheroid Oblate spheroidal coordinates Oblique projection Oblique reflection Observability Observability Gramian Observable subgroup… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”