References
Perron, O.: Die Lehre von den Kettenbrüchen. Chelsea Publ. Co. 1950.
Khintchine, A.: Metrische Kettenbruch-Probleme. Compositio Mathematica1, 361 (1935).
Neumann, J. v., andB. Tuckerman: Continued-Fraction Expansion of 21/3. Math. Tables and Other Aids to Computation9, 23 (1955).
Cramér, Harald: Mathematical Methods of Statistics. Princeton: University Press 1954.
Roth, K. F.: Rational Approximations to Algebraic Numbers. Mathematika2, 1 (1955) (with corrigendum on p. 168).
Weyl, H.: Über die Gleichverteilung von Zahlen mod. Eins. Math. Annalen77, 313 (1916).
Richtmyer, R. D.: The Evaluation of Definite Integrals, and a Quasi-Monte-Carlo Method based on the Properties of Algebraic Numbers. Los Alamos Scientific Laboratory Report LA-1342, 1951.
Richtmyer, R. D.: A Non-Random Sampling Method, based on Congruences, for “Monte Carlo” Problems. AEC Computing and Applied Mathematics Center, Report NYO-8674, New York University 1958.
Ostrowski, A.: Bemerkungen zur Theorie der diophantischen Approximationen. Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität1, 77 (1922).
Peck, L. G.: On Uniform Distribution of Algebraic Numbers. Proc. Amer. Math. Soc.4, 440 (1953).
Author information
Authors and Affiliations
Additional information
The work presented in this paper was supported by Los Alamos Scientific Laboratory, University of California, under Contract W-7405-Eng-36 with the U.S. Atomic Energy Commission and by the AEC Computing and Applied Mathematics Center, Institute of Mathematical Sciences, New York University, under Contract AT(30-1)-1480 with the U.S. Atomic Energy Commission.
Rights and permissions
About this article
Cite this article
Richtmyer, R.D., Devaney, M. & Metropolis, N. Continued fraction expansions of algebraic numbers. Numer. Math. 4, 68–84 (1962). https://doi.org/10.1007/BF01386297
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01386297