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Euclidean distance
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Overview
Use casemeasuring straight-line distance between two points in Euclidean space
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Last updatedUpdated 18h ago
WikidataQ913822
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Euclidean distance

concept

Straight-line distance between two points in Euclidean space, commonly used in vector similarity.

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named after

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Euclid of Alexandria○UnverifiedHighFresh1

based on

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Pythagorean theorem○UnverifiedHighFresh1

satisfies property

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metric space axioms○UnverifiedHighFresh1

formula

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sqrt(sum((xi - yi)^2)) for i=1 to n○UnverifiedHighFresh1

mathematical foundation

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Euclidean geometry○UnverifiedHighFresh1

primary use case

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measuring straight-line distance between two points in Euclidean space○UnverifiedHighFresh1

used in

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machine learning algorithms○UnverifiedHighFresh1
k-nearest neighbors algorithm○UnverifiedHighFresh1
clustering algorithms○UnverifiedHighFresh1

computational complexity

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O(n) where n is the number of dimensions○UnverifiedHighFresh1

alternative to

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Minkowski distance○UnverifiedHighFresh1
Manhattan distance○UnverifiedHighFresh1
Chebyshev distance○UnverifiedHighFresh1

Alternatives & Similar Tools

Minkowski distance
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Manhattan distance
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Chebyshev distance
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2 entities depend on Euclidean distance
K-Nearest Neighbors
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Claim count: 22Last updated: 4/17/2026Edit history