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  2. Distance from a point to a line - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    Learn how to calculate the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. See different formulas, proofs and examples for lines defined by equations, points or normals.

  3. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    Learn about the definition, formulas, properties and applications of Euclidean distance, the length of the line segment between two points in Euclidean space. Euclidean distance is a metric space that obeys the Pythagorean theorem and Ptolemy's inequality.

  4. Distance between two parallel lines - Wikipedia

    en.wikipedia.org/wiki/Distance_between_two...

    Learn how to calculate the distance between two parallel lines in the plane using linear systems and vector products. See the formula, the proof, and examples of non-vertical parallel lines.

  5. Hesse normal form - Wikipedia

    en.wikipedia.org/wiki/Hesse_normal_form

    Distance from the origin O to the line E calculated with the Hesse normal form. Normal vector in red, line in green, point O shown in blue. The Hesse normal form named after Otto Hesse, is an equation used in analytic geometry, and describes a line in or a plane in Euclidean space or a hyperplane in higher dimensions.

  6. Minkowski distance - Wikipedia

    en.wikipedia.org/wiki/Minkowski_distance

    Minkowski distance is a metric in a normed vector space that generalizes the Euclidean and Manhattan distances. It is named after Hermann Minkowski and has various applications in machine learning and AI.

  7. Frenet–Serret formulas - Wikipedia

    en.wikipedia.org/wiki/Frenet–Serret_formulas

    The T and N vectors at two points on a plane curve, a translated version of the second frame (dotted), and the change in T: δT'. δs is the distance between the points. In the limit d T d s {\displaystyle {\tfrac {d\mathbf {T} }{ds}}} will be in the direction N and the curvature describes the speed of rotation of the frame.

  8. Vincenty's formulae - Wikipedia

    en.wikipedia.org/wiki/Vincenty's_formulae

    Vincenty's formulae are methods to calculate the distance and azimuth between two points on a spheroid. They are based on Legendre, Bessel and Helmert's formulas and are accurate to within 0.5 mm on the Earth ellipsoid.

  9. Euler's theorem in geometry - Wikipedia

    en.wikipedia.org/wiki/Euler's_theorem_in_geometry

    Learn about Euler's theorem, which relates the distance between the circumcenter and incenter of a triangle to the circumradius and inradius. Find out its history, applications, and related inequalities in Euclidean and absolute geometry.

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