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In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.<?xml:namespace prefix = "o" ns = "urn:schemas-microsoft-com:office:office" />

The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number a/b is a "good" approximation of a real number α if the absolute value of the difference between a/b and α may not decrease if a/b is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of continued fractions.

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