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  2. Great-circle distance - Wikipedia

    en.wikipedia.org/wiki/Great-circle_distance

    A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. 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 ...

  3. Inversive distance - Wikipedia

    en.wikipedia.org/wiki/Inversive_distance

    For two circles in the Euclidean plane with radii and , and distance between their centers, the inversive distance can be defined by the formula [1] =. This formula gives: a value greater than 1 for two disjoint circles,

  4. Euler's theorem in geometry - Wikipedia

    en.wikipedia.org/wiki/Euler's_theorem_in_geometry

    In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively).

  5. Tangent lines to circles - Wikipedia

    en.wikipedia.org/wiki/Tangent_lines_to_circles

    The distances between the centers of the nearer and farther circles, O 2 and O 1 and the point where the two outer tangents of the two circles intersect (homothetic center), S respectively can be found out using similarity as follows: Here, r can be r 1 or r 2 depending upon the need to find distances from the centers of the nearer or farther ...

  6. Haversine formula - Wikipedia

    en.wikipedia.org/wiki/Haversine_formula

    The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation , it is a special case of a more general formula in spherical trigonometry , the law of haversines , that relates the sides and angles of spherical triangles.

  7. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is the start and which is the destination. [11] It is positive, meaning that the distance between every two distinct points is a positive number, while the distance from any point to itself is zero. [11]

  8. Taxicab geometry - Wikipedia

    en.wikipedia.org/wiki/Taxicab_geometry

    Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.

  9. Chord (geometry) - Wikipedia

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

    Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.

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