There is also the closely linked area of Diophantine approximations: given a number formula_35, then finding how well can it be approximated by rationals. (We are looking for approximations that are good relative to the amount of space that it takes to write the rational: call formula_61 (with formula_62) a good approximation to formula_35 if formula_64, where formula_65 is large.) This question is of special interest if formula_35 is an algebraic number. If formula_35 cannot be well approximated, then some equations do not have integer or rational solutions. Moreover, several concepts (especially that of height) turn out to be critical both in Diophantine geometry and in the study of Diophantine approximations. This question is also of special interest in transcendental number theory: if a number can be better approximated than any algebraic number, then it is a transcendental number. It is by this argument that Pi and e have been shown to be transcendental.