Definition:Euclidean Metric/Real Number Plane

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

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

where $x = \left({x_1, x_2}\right), y = \left({y_1, y_2}\right) \in \R^2$.

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

Also see

 * Definition:Euclidean Metric/Real Vector Space