'The mother of all continued fractions'
Tom 84 / 2000
Colloquium Mathematicum 84 (2000), 109-123
DOI: 10.4064/cm-84/85-1-109-123
Streszczenie
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.
