## Liouville's Rational Approximation Theorem

For any Algebraic Number of degree , a Rational approximation must satisfy

for sufficiently large . Writing leads to the definition of the Liouville-Roth Constant of a given number.

See also Lagrange Number (Rational Approximation), Liouville's Constant, Liouville Number, Liouville-Roth Constant, Markov Number, Roth's Theorem, Thue-Siegel-Roth Theorem

References

Courant, R. and Robbins, H. Liouville's Theorem and the Construction of Transcendental Numbers.'' §2.6.2 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 104-107, 1996.