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Euclidean distance

Index Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. [1]

33 relations: Absolute value, Cartesian coordinate system, Chebyshev distance, Displacement (vector), Distance, Dot product, Euclidean distance matrix, Euclidean geometry, Euclidean space, Euclidean vector, Generalization, Haversine formula, Line (geometry), Line segment, Lp space, Mathematics, Metric (mathematics), Metric space, Minkowski distance, Norm (mathematics), Origin (mathematics), Point (geometry), Polar coordinate system, Pythagorean addition, Pythagorean theorem, Rational trigonometry, Real line, Real number, Taxicab geometry, Translation (geometry), Triangle inequality, Two-dimensional space, Vincenty's formulae.

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Chebyshev distance

In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension.

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Displacement (vector)

A displacement is a vector whose length is the shortest distance from the initial to the final position of a point P. It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point.

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Distance is a numerical measurement of how far apart objects are.

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Dot product

In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.

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Euclidean distance matrix

In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space.

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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A generalization (or generalisation) is the formulation of general concepts from specific instances by abstracting common properties.

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Haversine formula

The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

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Lp space

In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Metric (mathematics)

In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.

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Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

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Minkowski distance

The Minkowski distance is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.

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Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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Pythagorean addition

In mathematics, Pythagorean addition is the following binary operation on the real numbers: The name recalls the Pythagorean theorem, which states that the length of the hypotenuse of a right triangle is where a and b are the lengths of the other sides.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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Rational trigonometry

Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales.

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Real line

In mathematics, the real line, or real number line is the line whose points are the real numbers.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Taxicab geometry

A taxicab geometry is a form of geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates.

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Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.

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Triangle inequality

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

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Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

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Vincenty's formulae

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).

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Euclidean Distance, Euclidean length, Euclidean metric, Euclidian distance, Geometric distance, Pythagorean distance, Pythagorean metric.


[1] https://en.wikipedia.org/wiki/Euclidean_distance

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