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Euclidean (or, less commonly, Euclidian) is an adjective derived from the name of Euclid, an ancient Greek mathematician. It may refer to:


  • Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations
  • Euclidean geometry, the study of the properties of Euclidean spaces
  • Non-Euclidean geometry, systems of points, lines, and planes analogous to Euclidean geometry but without uniquely determined parallel lines
  • Euclidean distance, the distance between pairs of points in Euclidean spaces
  • Euclidean ball, the set of points within some fixed distance from a center point

Number theory[edit]

  • Euclidean division, the division which produces a quotient and a remainder
  • Euclidean algorithm, a method for finding greatest common divisors
  • Extended Euclidean algorithm, a method for solving the Diophantine equation ax + by = d where d is the greatest common divisor of a and b.
  • Euclid's lemma: if a prime number divides a product of two numbers, then it divides at least one of those two numbers.
  • Euclidean domain, a ring in which Euclidean division may be defined, which allows Euclid's lemma to be true and the Euclidean algorithm and the extended Euclidean algorithm to work


See also[edit]