For example, whilst the location of a fixed point on some curved line may be given by a set of numbers whose values depend on how the curve is parametrized, the length (appropriately defined) of the curve between "two" such fixed points will be independent of the particular choice of parametrization (in this case: the method by which an arbitrary point on the line is uniquely indexed). The length of the curve is therefore a parameterization-invariant quantity. In such cases parameterization is a mathematical tool employed to extract a result whose value does not depend on, or make reference to, the details of the parameterization. More generally, parametrization invariance of a physical theory implies that either the dimensionality or the volume of the parameter space is larger than is necessary to describe the physics (the quantities of physical significance) in question.