In mathematics, the Euclidean distance between two points in Euclidean space is a number, the length of a line segment between the two points.
It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and is occasionally called the Pythagorean distance.
These names come from the ancient Greek mathematicians Euclid and Pythagoras, but Euclid did not represent distances as numbers, and the connection from the Pythagorean theorem to distance calculation was not made until the 17th century.
The distance between two objects that are not points is usually defined to be the smallest distance between any two points from the two objects.
Formulas are known for computing distances between different types of objects, such as the distance from a point to a line.
In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied.
The square of the Euclidean distance is not a metric, but is convenient for many applications in statistics and optimization.
