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:
 * $\displaystyle d_2 \left({x, y}\right) := \sqrt{\left({x_1 - y_1}\right)^2 + \left({x_2 - y_2}\right)^2 + \left({x_3 - y_3}\right)^2}$

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

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

Also see

 * Definition:Euclidean Metric/Real Vector Space