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ArticleOriginal scientific text

Title

'The mother of all continued fractions'

Authors 1, 2

Affiliations

  1. Universiteit Utrecht, Fac. Wiskunde en Informatica and MRI, Budapestlaan 6, P.O. Box 80.000, 3508 TA Utrecht, the Netherlands
  2. Technische Universiteit Delft, ITS (SSOR) Thomas Stieltjes Institute for Mathematics, Mekelweg 4, 2628 CD Delft, the Netherlands

Abstract

We give the relationship between regular continued fractions and Lehner fractions, using a procedure known as insertion}. Starting from the regular continued fraction expansion of any real irrational x, when the maximal number of insertions is applied one obtains the Lehner fraction of x. Insertions (and singularizations) show how these (and other) continued fraction expansions are related. We also investigate the relation between Lehner fractions and the Farey expansion (also known as the full continued fraction), and obtain the ergodic system underlying the Farey expansion.

Keywords

ENG
insertion, ergodic theory, continued fractions, singularization

Bibliography

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Colloquium Mathematicum
2000/84/85/1
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Pages:
109-123
Main language of publication
English
Received
1999-05-25
Accepted
1999-09-22
Published
2000
Exact and natural sciences