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On the continued fraction algorithm

Published online by Cambridge University Press:  17 April 2009

J. M. Mack
J. M. Mack
Affiliation:
University of Sydney, Sydney, New South Wales.
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Abstract

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The fact that continued fractions can be described in terms of Farey sections is used to obtain a generalised continued fraction algorithm. Geometrically, the algorithm transfers the continued fraction process from the real line R to an arbitrary rational line l in Rn. Arithmetically, the algorithm provides a sequence of simultaneous rational approximations to a set of n real numbers θ1, …, θn in the extreme case where all of the numbers are rationally dependent on 1 and (say) θ1. All but a finite number of best approximations are given by the algorithm.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 3 , December 1970 , pp. 413 - 422
Copyright
Copyright © Australian Mathematical Society 1970

References

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