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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.

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Osculating_plane — Please support Wikipedia.
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 304 videos foundNext >
 Normal, Osculating, and Rectifying PlanesNormal, Osculating, and Rectifying Planes. D Block - Multivariable Calculus - 9/28/11We talk about unit tangent vectors, principle unit normal vector, and binormal vectors, osculating planes, and normal planes. Lecture 2011.07.08 Part 04/6 Osculating Plane: Finding an EquationOsculating plane: finding an equation. Lecturer: Nikolay Brodskiy https://sites.google.com/site/calcuplus/ This video on my site: http://goo.gl/2tQNT. Normal and Osculating PlanesCalculus 3, Arc Length and Curvature, Tangent Normal and Binormal Vectors, Normal and Osculating Planes. MATH 202 Chapter 2 Osculating plane and circle Lecture 2011.07.08 Part 01/6 Finding the Osculating Circle for a Planar CurveFinding the osculating circle for a planar curve. Lecturer: Nikolay Brodskiy https://sites.google.com/site/calcuplus/ This video on my site: http://goo.gl/ilgMe. Lecture 2011.07.08 Part 05/6 Osculating Plane from Physics Point of ViewOsculating plane from Physics point of view. Lecturer: Nikolay Brodskiy https://sites.google.com/site/calcuplus/ This video on my site: http://goo.gl/SD2C2. MathHistory16: Differential GeometryDifferential geometry arises from applying calculus and analytic geometry to curves and surfaces. This video begins with a discussion of planar curves and th... Fundamental Unit Vector and Fundamental Plane Lecture by Miss. Megha Sharma.The unit vector along tangent, principal normal, and binormal are denoted by t^,n^,b^ and form an orthogonal right handed triad so we can say that t^.n^ =0, ... osculating circlethe curvature of a parabola changes in time.
 304 videos foundNext >

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