Page "World line" Paragraph 10

A one-dimensional line or curve can be represented by the coordinates as a function of one parameter.

Each value of the parameter corresponds to a point in spacetime and varying the parameter traces out a line.

So in mathematical terms a curve is defined by four coordinate functions ( where usually denotes the time coordinate ) depending on one parameter.

A coordinate grid in spacetime is the set of curves one obtains if three out of four coordinate functions are set to a constant.