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  2. Archimedean spiral - Wikipedia

    en.wikipedia.org/wiki/Archimedean_spiral

    A mechanical method for constructing the arithmetic spiral uses a modified string compass, where the string wraps and winds (or unwraps/unwinds) about a fixed central pin (that does not pivot), thereby incrementing (or decrementing) the length of the radius (string) as the angle changes (the string winds around the fixed pin which does not pivot).

  3. Meridian arc - Wikipedia

    en.wikipedia.org/wiki/Meridian_arc

    On an ellipsoid of revolution, for short meridian arcs, their length can be approximated using the Earth's meridional radius of curvature and the circular arc formulation. For longer arcs, the length follows from the subtraction of two meridian distances, the distance from the equator to a point at a latitude φ.

  4. Arc length - Wikipedia

    en.wikipedia.org/wiki/Arc_length

    These curves are called rectifiable and the arc length is defined as the number . A signed arc length can be defined to convey a sense of orientation or "direction" with respect to a reference point taken as origin in the curve (see also: curve orientation and signed distance). [2]

  5. List of common coordinate transformations - Wikipedia

    en.wikipedia.org/wiki/List_of_common_coordinate...

    2.4 Arc-length, curvature and torsion from Cartesian coordinates. 3 See also. 4 References. Toggle the table of contents. List of common coordinate transformations. 3 ...

  6. 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 ...

  7. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    There are ways of describing curves without coordinates, using intrinsic equations that use invariant quantities such as curvature and arc length. These include: The Whewell equation relates arc length and the tangential angle. The Cesàro equation relates arc length and curvature.

  8. Great-circle distance - Wikipedia

    en.wikipedia.org/wiki/Great-circle_distance

    The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...

  9. Geographical distance - Wikipedia

    en.wikipedia.org/wiki/Geographical_distance

    The slant distance s (chord length) between two points can be reduced to the arc length on the ellipsoid surface S as: [21] = (+) / / where R is evaluated from Earth's azimuthal radius of curvature and h are ellipsoidal heights are each point. The first term on the right-hand side of the equation accounts for the mean elevation and the second ...