What is Two-dimensional Euclidean space?

Two-dimensional Euclidean space or simply two-dimensional space is a geometric setting in which two values are required to determine the position of an element on the plane. The set R 2 {\displaystyle \mathbb {R} ^{2}} of pairs of real numbers with appropriate structure often serves as the canonical example of a Euclidean plane, the two-dimensional Euclidean space; for a generalization of the concept, see dimension. Two-dimensional space can be seen as a projection of the physical universe onto a plane. Usually, it is thought of as a Euclidean space and the two dimensions are called length and width.