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osculating circle
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The curvature at each point of a line is defined to be 1/r, where r is the radius of the osculating, or “kissing,” circle that best approximates the line at the given point.
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osculating circle

mathematics

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differential geometry

  • An annular strip (the region between two concentric circles) can be cut and bent into a helical strake that follows approximately the contour of a cylinder. Techniques of differential geometry are employed to find the dimensions of the annular strip that will best match the required curvature of the strake.
    In differential geometry: Curvature of curves

    …shown in the figure) the osculating circle, from the Latin osculare (“to kiss”). He then defined the curvature of the curve (and the circle) as 1/r, where r is the radius of the osculating circle. As a curve becomes straighter, a circle with a larger radius must be used to…

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