dimension of an algebraic variety

In mathematics, the dimension of an algebraic variety V in algebraic geometry is defined, informally speaking, as the number of independent rational functions that exist on V. For example, an algebraic curve has by definition dimension 1. That means that any two rational functions F and G on it must satisfy some polynomial relation P(F,G) = 0. This implies that F and G are constrained to take related values (up to some finite freedom of choice): they cannot be truly independent.
See more at Wikipedia.org...