Paper #171

Title:

Approximation of quadratic irrationals and their pierce expansions

Authors:

Jaume Paradís, Lluís Bibiloni and Pelegrí Viader

Date:

June 1996

Abstract:

In this article two aims are pursued: on the one hand, to present a rapidly converging algorithm for the approximation of square roots; on the other hand and based on the previous algorithm, to find the Pierce expansions of a certain class of quadratic irrationals as an alternative way to the method presented in 1984 by J.O. Shallit; we extend the method to find also the Pierce expansions of quadratic irrationals of the form $2 (p-1) (p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.

Keywords:

Quadratic irrationals, Pierce series

JEL codes:

C00

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

The Fibonacci Quarterly, 36, 2, (1998), pp. 146-153

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