If we denote the coordinates of a point in Minkowski space as , then the distance squared between *p* and the origin is defined as

The signs of the four terms correspond to the signature of the metric. Notice that the right side may be negative, making the distance imaginary.

Around 1907 Hermann Minkowski realized that the special theory of relativity, introducted by Albert Einstein in 1905 could be mathematically described using a four-dimensional spacetime, which combines the dimension of time with the three space dimensions. The Lorentz transformations of special relativity can be represented as generalized rotations of the Minkowski space.

- Cartesian space
- generalized rotations - SO(1,3) being the Lorentz group of transformations
- metric tensor
- Erlanger program