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Approximating to a Square Root

Published online by Cambridge University Press:  03 November 2016

R.F. Muirhead
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Extract

The method explained by Dr. C. V Boys has great merit. I for one fully sympathise with his preference for vulgarity in fractions. What here follows is meant to be to some extent supplementary to Dr. Boys’ article.

If we denote by P1/Q1, P2/Q2, … the successive convergents to √M in Dr. Boys’ series which are arithmetic means, and P1= p, Q1=q, the law connecting them is

Pr+1=Pr2+MQr2, Qr+1=2PrQr.

Type
Research Article
Information
The Mathematical Gazette , Volume 17 , Issue 223 , May 1933 , pp. 84 - 86
Copyright
Copyright © The Mathematical Association 1933

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References

* Math.Gazette, XVI (May, 1932), p. 111.