\begin{definition}[Definition:Euclidean Metric/Real Number Plane]
Let $\R^2$ be the real number plane.
The '''Euclidean metric''' on $\R^2$ is defined as:
:$\ds \map {d_2} {x, y} := \sqrt {\paren {x_1 - y_1}^2 + \paren {x_2 - y_2}^2}$
where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in \R^2$.
\end{definition}