In mathematics , the Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula . By using this formula as distance, Euclidean space (or even any inner product space ) becomes a metric space . The associated norm is called the Euclidean norm . Older literature refers to the metric as Pythagorean metric. Contents ). 1 , p 2 ,..., p n 1 , q 2 ,..., q n where the last equation involves the dot product .
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