osculating curve wikipedia - EAS

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  1. Wikipedia Osculating curve Osculating curve is a plane curve from a given family that has the highest possible order of contact with another curve.
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    What is the osculating circle of a curve?
    In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p.
    en.wikipedia.org/wiki/Osculating_circle
    What does osculation mean in math?
    The concept of osculation can be generalized to higher-dimensional spaces, and to objects that are not curves within those spaces. For instance an osculating plane to a space curve is a plane that has second-order contact with the curve. This is as high an order as is possible in the general case.
    en.wikipedia.org/wiki/Osculating_curve
    When do analytic curves osculate at a point?
    In one dimension, analytic curves are said to osculate at a point if they share the first three terms of their Taylor expansion about that point. This concept can be generalized to superosculation, in which two curves share more than the first three terms of their Taylor expansion.
    en.wikipedia.org/wiki/Osculating_curve
    What is the osculating plane in geometry?
    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.
    en.wikipedia.org/wiki/Osculating_plane
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    https://en.wikipedia.org/wiki/Osculating_curve

    In differential geometry, an osculating curve is a plane curve from a given family that has the highest possible order of contact with another curve. That is, if F is a family of smooth curves, C is a smooth curve (not in general belonging to F), and p is a point on C, then an osculating curve from F at p is a

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    Examples of osculating curves of different orders include:
    • The tangent line to a curve C at a point p, the osculating curve from the family of straight lines. The tangent line shares its first derivative (

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    The concept of osculation can be generalized to higher-dimensional spaces, and to objects that are not curves within those spaces. For instance an osculating plane to a space curve is a plane that has second-order contact with the curve. This is as high an order as is

     ...

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  5. https://en.wikipedia.org/wiki/Osculating_circle

    In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p. Its center lies on the inner normal line, and its curvaturedefines the curvature of the given curve at that point. This circle, which is the o…

  6. https://en.wikipedia.org/wiki/Talk:Osculating_curve

    Talk:Osculating curve. Jump to navigation Jump to search. WikiProject Mathematics (Rated Start-class, Mid-priority) This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the ...

  7. https://en.wikipedia.org/wiki/Osculating_plane

    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.

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    • https://en.wikipedia.org/wiki/Osculating_orbit

      In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturbations were absent.

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      • https://en.wikipedia.org/wiki/Curvature

        Historically, the curvature of a differentiable curve was defined through the osculating circle, which is the circle that best approximates the curve at a point. More precisely, given a point P on a curve, every other point Q of the curve defines a circle (or sometimes a line) passing through Q and tangent to the curve at P.

      • https://en.wikipedia.org/wiki/Talk:Osculating_circle

        Osculate literally means to kiss; the term is used because osculation is a more gentle form of contact than simple tangency. I am not sure the word "gentle" is the best.

      • https://simple.wikipedia.org/wiki/File:Osculating_circle.svg

        osculation Usage on eo.wikipedia.org Kurbeco (kurbo) Plurvariabla kalkulo Usage on es.wikipedia.org Geometría diferencial de curvas Cálculo multivariable Usage on et.wikipedia.org Kõverus Usage on eu.wikipedia.org Zirkulu oskulatzaile Kurbadura Usage on fa.wikipedia.org ریاضیات حساب چندمتغیره Usage on fi.wikipedia.org Matematiikka Kaarevuus

      • Wikizero - Osculating curve

        https://wikizero.com/www//Osculating_curve

        In differential geometry, an osculating curve is a plane curve from a given family that has the highest possible order of contact with another curve.

      • https://wikimili.com/en/Osculating_circle

        In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p.



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