In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, four-dimensional space ("4D") is an abstract concept derived by generalizing the rules of three-dimensional space

Three-dimensional space

Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...

. It has been studied by mathematicians and philosophers for almost three hundred years, both for its own interest and for the insights it offered into mathematics and related fields.

Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions.