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Wikipedia Description

In mathematics, the Euclidean distance or Euclidean metric is the ordinary (i.e straight line) distance between two points in Euclidean space. With this distance, Euclidean space becomes a metric space. The associated norm is called the Euclidean norm. Older literature refers to the metric as Pythagorean metric . The Euclidean distance between points p and q is the length of the line segment connecting them ( ). In Cartesian coordinates, if p =( p 1, p 2 ,..., p n ) and q =( q 1, q 2 ,..., q n ) are two points in Euclidean n -space, then the distance (d) from p to q, or from q to p is given by the Pythagorean formula : ( 1 ) The position of a point in a Euclidean n -space is a Euclidean vector. So, p and q are Euclidean vectors, starting from the origin of the space, and their tips indicate two points. The Euclidean norm, or Euclidean length, or magnitude of a vector measures the length of the vector:

euclid, length, mathematics