# Euclidean distance

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## English

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### Noun

Euclidean distance (countable and uncountable, plural Euclidean distances)

1. (geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (ax, ay) and b = (bx, by) is defined as:
${\displaystyle d({\textbf {a}},{\textbf {b}})={\sqrt {({\textbf {a}}_{x}-{\textbf {b}}_{x})^{2}+({\textbf {a}}_{y}-{\textbf {b}}_{y})^{2}}}}$