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.

Also see

 * Definition:Euclidean Metric/Real Vector Space