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  2. Degree of curvature - Wikipedia

    en.wikipedia.org/wiki/Degree_of_curvature

    Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈ 5729.57795, where D is degree and r is radius. Since rail routes have very large radii, they are laid out in chords, as the difference to the arc is inconsequential; this made work easier before electronic ...

  3. 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 ...

  4. Principal curvature - Wikipedia

    en.wikipedia.org/wiki/Principal_curvature

    This curve will in general have different curvatures for different normal planes at p. The principal curvatures at p, denoted k 1 and k 2, are the maximum and minimum values of this curvature. Here the curvature of a curve is by definition the reciprocal of the radius of the osculating circle. The curvature is taken to be positive if the curve ...

  5. List of graphs by edges and vertices - Wikipedia

    en.wikipedia.org/wiki/List_of_graphs_by_edges...

    The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number) and χ' (chromatic index) are also sortable, allowing to search for a parameter or another.

  6. Gaussian function - Wikipedia

    en.wikipedia.org/wiki/Gaussian_function

    The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".

  7. List of curves - Wikipedia

    en.wikipedia.org/wiki/List_of_curves

    Print/export Download as PDF; Printable version; In other projects ... Plane curves of degree 2 are known as conics or conic sections and include Circle. Unit circle;

  8. Euler spiral - Wikipedia

    en.wikipedia.org/wiki/Euler_spiral

    A double-end Euler spiral. The curve continues to converge to the points marked, as t tends to positive or negative infinity. An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.

  9. Curve of constant width - Wikipedia

    en.wikipedia.org/wiki/Curve_of_constant_width

    Some curves, such as ellipses, have exactly four vertices, but this is not possible for a curve of constant width. [14] [23] Because local minima of curvature are opposite local maxima of curvature, the only curves of constant width with central symmetry are the circles, for which the curvature is the same at all points. [13]

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