A geometrical approach to approximations by continued fractions

Author:

Kopetzky H. G.,Schnitzer F. J.

Abstract

AbstractBy simple geometrical considerations new proofs for some classical results are given and also new theorems about approximation by continued fractions are derived. This geometrical approach presents an instructive visualisation of the nature of proximation theorems.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference13 articles.

1. On two theorems of Kopetzky and Schnitzer on the approximation of continued fractions;Tong;J. Reine Angew. Math.,1985

2. Remarques sur certaines suites d'approximation;Humbert;J. Math. Pures Appl.,1916

3. Bemerkung zur Theorie der Approximation der irrationalen Zahlen durch rationale Zahlen;Fujiwara;Tôhoku Math. J.,1918

4. Bemerkungen zu einem Approximationssatz für regelmässige Kettenbrüche;Kopetzky;J. Reine Angew. Math.,1977

5. Über Näherungswerte und Kettenbrüche;Vahlen;J. Reine Angew. Math.,1859

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1. Robinson's Theorem on Asymmetric Diophantine Approximation;Rocky Mountain Journal of Mathematics;1996-03-01

2. The Best Approximation Function to Irrational Numbers;Journal of Number Theory;1994-10

3. Diophantine approximation of a single irrational number;Journal of Number Theory;1990-05

4. On the approximation by continued fractions;Indagationes Mathematicae (Proceedings);1989-09

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