Definition:Euclidean Metric/Ordinary Space

Definition
Let $\R^3$ be the real vector space representation of ordinary $3$d space.

The Euclidean metric on $\R^3$ is defined as:
 * $\map {d_2} {x, y} := \sqrt {\paren {x_1 - y_1}^2 + \paren {x_2 - y_2}^2 + \paren {x_3 - y_3}^2}$

where $x = \tuple {x_1, x_2, x_3}, y = \tuple {y_1, y_2, y_3} \in \R^3$.

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

Also see

 * Definition:Euclidean Metric/Real Vector Space