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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.
Learn how to calculate the distance between two points on the Earth's surface using different approximations and formulae. Compare flat, spherical and ellipsoidal models and their errors and limitations.
Euclidean distance is the length of the line segment between two points in Euclidean space. It can be calculated from the Cartesian coordinates using the Pythagorean theorem, and has various properties and applications in mathematics and statistics.
The haversine formula is a computationally efficient way to calculate the great-circle distance between two points on a sphere, using the chord length of unit sphere. It is accurate for short distances and avoids the rounding errors of the spherical law of cosines formula.
Distance is a numerical or qualitative measurement of how far apart objects, points, people, or ideas are. Learn about different types of distances in physics, geometry, mathematics, and social sciences, with formulas, diagrams, and applications.
Learn how comoving and proper distances are defined and used in cosmology to measure distances between objects in an expanding universe. See formulas, examples, diagrams and references.
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
Learn how to calculate the distance from a point to a plane in Euclidean space using coordinate or vector formulas. See the proof that the point on the plane closest to the origin is the orthogonal projection of the given point.
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