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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. Radius of curvature (optics) - Wikipedia

    en.wikipedia.org/wiki/Radius_of_curvature_(optics)

    Radius of curvature sign convention for optical design. Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis.

  4. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    The mean curvature is an extrinsic measure of curvature equal to half the sum of the principal curvatures, ⁠ k 1 + k 2 / 2 ⁠. It has a dimension of length −1. Mean curvature is closely related to the first variation of surface area. In particular, a minimal surface such as a soap film has mean curvature zero and a soap bubble has

  5. 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 ...

  6. Principal curvature - Wikipedia

    en.wikipedia.org/wiki/Principal_curvature

    The product k 1 k 2 of the two principal curvatures is the Gaussian curvature, K, and the average (k 1 + k 2)/2 is the mean curvature, H. If at least one of the principal curvatures is zero at every point, then the Gaussian curvature will be 0 and the surface is a developable surface. For a minimal surface, the mean curvature is zero at every ...

  7. Sagitta (optics) - Wikipedia

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

    Deep blue ray refers the radius of curvature and the red line segment is the sagitta of the curve (black). In optics and especially telescope making, sagitta or sag is a measure of the glass removed to yield an optical curve. It is approximated by the formula (),

  8. Osculating circle - Wikipedia

    en.wikipedia.org/wiki/Osculating_circle

    The parabola has fourth order contact with its osculating circle there. For large t the radius of curvature increases ~ t 3, that is, the curve straightens more and more.

  9. Focal length - Wikipedia

    en.wikipedia.org/wiki/Focal_length

    For a spherically-curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. The focal length is positive for a concave mirror, and negative for a convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so