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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. Track geometry - Wikipedia

    en.wikipedia.org/wiki/Track_geometry

    The degree of curvature is inverse of radius. The larger the degree of curvature, the sharper the curve is. Expressing the curve in this way allows surveyors to use estimation and simpler tools in curve measurement. This can be done by using a 62-foot (18.90 m) string line to be a chord to connect the arc at the gauge side of the reference rail.

  5. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    In Tractatus de configurationibus qualitatum et motuum, [1] the 14th-century philosopher and mathematician Nicole Oresme introduces the concept of curvature as a measure of departure from straightness; for circles he has the curvature as being inversely proportional to the radius; and he attempts to extend this idea to other curves as a continuously varying magnitude.

  6. Graph paper - Wikipedia

    en.wikipedia.org/wiki/Graph_paper

    Hexagonal paper shows regular hexagons instead of squares. These can be used to map geometric tiled or tesselated designs among other uses. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.

  7. Exoplanet orbital and physical parameters - Wikipedia

    en.wikipedia.org/wiki/Exoplanet_orbital_and...

    When the size of a planet is described using its radius, this is approximating the shape by a sphere. However, the rotation of a planet causes it to be flattened at the poles; so the equatorial radius is larger than the polar radius, making it closer to an oblate spheroid. The oblateness of transiting exoplanets will affect the transit light ...

  8. Reuleaux triangle - Wikipedia

    en.wikipedia.org/wiki/Reuleaux_triangle

    Its width, approximately 1.54, is the root of a degree-6 polynomial with integer coefficients. [17] [19] [20] Just as it is possible for a circle to be surrounded by six congruent circles that touch it, it is also possible to arrange seven congruent Reuleaux triangles so that they all make contact with a central Reuleaux triangle of the same size.

  9. Curve of constant width - Wikipedia

    en.wikipedia.org/wiki/Curve_of_constant_width

    A curve of constant width defined by an 8th-degree polynomial. Circles have constant width, equal to their diameter. On the other hand, squares do not: supporting lines parallel to two opposite sides of the square are closer together than supporting lines parallel to a diagonal. More generally, no polygon can have constant width. However, there ...

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