# 'The mother of all continued fractions'

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 1, page 109-123
- ISSN: 0010-1354

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topDajani, Karma, and Kraaikamp, Cor. "'The mother of all continued fractions'." Colloquium Mathematicae 84/85.1 (2000): 109-123. <http://eudml.org/doc/210790>.

@article{Dajani2000,

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.},

author = {Dajani, Karma, Kraaikamp, Cor},

journal = {Colloquium Mathematicae},

keywords = {insertion; ergodic theory; continued fractions; singularization; semi-regular continued fractions},

language = {eng},

number = {1},

pages = {109-123},

title = {'The mother of all continued fractions'},

url = {http://eudml.org/doc/210790},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Dajani, Karma

AU - Kraaikamp, Cor

TI - 'The mother of all continued fractions'

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 1

SP - 109

EP - 123

AB - 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.

LA - eng

KW - insertion; ergodic theory; continued fractions; singularization; semi-regular continued fractions

UR - http://eudml.org/doc/210790

ER -

## References

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