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Continued Fractions in Several Dimensions

Published online by Cambridge University Press:  24 October 2008

R. E. A. C. Paley  and
H. D. Ursell
R. E. A. C. Paley
Affiliation:
Trinity College
H. D. Ursell
Affiliation:
Trinity College
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Extract

Continued fractions were generalised to more than one dimension by Jacobi and others: later Perron gave an account of the existing state of the subject with a detailed discussion of periodic fractions. Quite recently the subject has been attacked afresh by Mr. Maunsell

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 26 , Issue 2 , April 1930 , pp. 127 - 144
Copyright
Copyright © Cambridge Philosophical Society 1930

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References

* Math. Ann. 64 (1907), p. 1, q.v. for references to earlier literature.CrossRefGoogle Scholar

† Maunsell, F. G., Proc. Lond. Math. Soc. (2) 30 (1929), 127.Google Scholar

* The case mentioned above is an exception.

* In more than two dimensions we choose the greatest possible divisor at each stage.

* If the value of the c. f. be given geometrically by

so that r<a, β<a<(K+1)β, we find that the error of Jn is at least as big as

.

* Although not for cyclic fractions.