5 papers
Sharpening Borel's result in Diophantine approximation
Savita S. Adhin, Ayreena Bakhtawar, Cor Kraaikamp
In this paper, we refine Borel's 1903 result in Diophantine approximation by providing sharper bounds for the minimum of three consecutive approximation coefficients , def…
A strange continued fraction associated with the Romik map
Yufei Chen, Karma Dajani, Yanyan Hu +1
In 2008, Dan Romik studied in this journal Primitive Pythagorean Triples, or PPTs. In order to do so, he introduced a modified slow (subtractive) Euclidean algorithm, and showed th…
A unifying theory for metrical results on regular continued fraction convergents and mediants
Karma Dajani, Cor Kraaikamp, Slade Sanderson
We revisit Ito's (\cite{I1989}) natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational. With a sligh…
Sharpening Vahlen's result in Diophantine approximation
Ayreena Bakhtawar, Cor Kraaikamp
n this paper we refine Vahlen's 1895 result in Diophantine approximation by providing sharper bounds for the approximation coefficients, especially when at least one of the partial…
Inducing contractions of the mother of all continued fractions
Karma Dajani, Cor Kraaikamp, Slade Sanderson
We introduce a new, large class of continued fraction algorithms producing what are called contracted Farey expansions. These algorithms are defined by coupling two acceleration te…