Definition:Euclidean Metric/Real Number Plane

Definition
Let $\R^2$ be the real number plane.

The Euclidean metric on $\R^2$ is defined as:
 * $\displaystyle \map {d_2} {x, y} := \sqrt {\paren {x_1 - y_1}^2 + \paren {x_2 - y_2}^2}$

where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in \R^2$.

Also known as
The Euclidean metric is sometimes also referred to as the usual metric.

The real number plane with the Euclidean metric is also known as the Euclidean plane, but in the field of abstract geometry that term is used fora specific construct.

Also see

 * Definition:Euclidean Metric/Real Vector Space