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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.
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.
Learn about the shortest path algorithm invented by Edsger W. Dijkstra in 1956 and its applications in graph theory and network routing. See the algorithm's pseudocode, history, complexity, and examples.
Taxicab geometry or Manhattan geometry is a metric space where the distance between two points is the sum of the absolute differences of their coordinates. Learn about its history, spheres, arc length, and applications in regression analysis and non-Euclidean geometry.
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.
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 about the TSP, a classic optimization problem that asks for the shortest route visiting each city once. Find out its history, applications, and algorithms, including the Christofides-Serdyukov algorithm.
A metric or distance function is a function d which takes pairs of points or objects to real numbers and satisfies the following rules: The distance between an object and itself is always zero. The distance between distinct objects is always positive. Distance is symmetric: the distance from x to y is always the same as the distance from y to x.
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