What is 4-dimensional Euclidean space?
Euclidean space is the generalization of 2- and 3-dimensional spaces studied by the Greek mathematician Euclid, to any finite number of dimensions. It encompasses the concepts of length and angles. Two-dimensional Euclidean space is like a flat plane, where every point is located by two coordinates. There is only width and height in 2-dimensional space. There are two perpendicular directions in 2D space. Three-dimensional space is like the space we live in, where every point is located by three coordinates. There is height, width, and also depth in 3-dimensional space. There are 3 mutually perpendicular directions in 3D space. Likewise, 4-dimensional Euclidean space is one where every point is located by four coordinates. Not only there is height, width, and depth, there is also a fourth quantity that describes 4D thickness. There are 4 mutually perpendicular directions in 4D space.
