As Lagrange showed, any Irrational Number has an infinity of rational approximations
which satisfy

(1) |

(2) |

(3) |

(4) |

**References**

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.* New York: Dover, p. 40, 1987.

Chandrasekharan, K. *An Introduction to Analytic Number Theory.* Berlin: Springer-Verlag, p. 23, 1968.

Conway, J. H. and Guy, R. K. *The Book of Numbers.* New York: Springer-Verlag, pp. 187-189, 1996.

© 1996-9

1999-05-25