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  2. Radius of curvature - Wikipedia

    en.wikipedia.org/wiki/Radius_of_curvature

    Radius of curvature and center of curvature. In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or ...

  3. Osculating circle - Wikipedia

    en.wikipedia.org/wiki/Osculating_circle

    The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point. A geometric construction was described by Isaac Newton in his Principia:

  4. Curve radius - Wikipedia

    en.wikipedia.org/wiki/Curve_radius

    Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Radius of curvature, the reciprocal of the ...

  5. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    The curvature is the reciprocal of radius of curvature. That is, the curvature is =, where R is the radius of curvature [5] (the whole circle has this curvature, it can be read as turn 2π over the length 2π R). This definition is difficult to manipulate and to express in formulas.

  6. Menger curvature - Wikipedia

    en.wikipedia.org/wiki/Menger_curvature

    In mathematics, the Menger curvature of a triple of points in n-dimensional Euclidean space R n is the reciprocal of the radius of the circle that passes through the three points. It is named after the Austrian - American mathematician Karl Menger .

  7. Sagitta (geometry) - Wikipedia

    en.wikipedia.org/wiki/Sagitta_(geometry)

    In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...

  8. Parallel curve - Wikipedia

    en.wikipedia.org/wiki/Parallel_curve

    The principal radii of curvature are the eigenvalues of the inverse of the shape operator, the principal curvature directions are its eigenvectors, the reciprocal of the Gaussian curvature is its determinant, and the mean radius of curvature is half its trace. Note the similarity to the geometric properties of general offset curves.

  9. Category:Curvature (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Category:Curvature...

    This page was last edited on 5 November 2024, at 17:14 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.