# Euclidean plane

## Geometric model of the planar projection of the physical universe / From Wikipedia, the free encyclopedia

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In mathematics, a **Euclidean plane** is a Euclidean space of dimension two, denoted ${\textbf {E}}^{2}$ or $\mathbb {E} ^{2}$. It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has also metrical properties induced by a distance, which allows to define circles, and angle measurement.

A Euclidean plane with a chosen Cartesian coordinate system is called a *Cartesian plane*.
The set $\mathbb {R} ^{2}$ of the ordered pairs of real numbers (the real coordinate plane), equipped with the dot product, is often called *the Euclidean plane*, since every Euclidean plane is isomorphic to it.