PROBLEM: Periodicity in Continued Fractions

Investigations of the length of the periods of quadratic irrationals.

INVESTIGATOR: Marius Beceanu

DESCRIPTION:  This paper seeks to recapitulate the known facts about the length of the
period of the continued fraction expansion of $\sqrt n$ as a function of $n$ and to make a few
(possibly) original contributions. I have established a result concerning the average period length
for $k<\sqrt n<k+1$, where $k$ is an integer, and, following numerical experiments, tried to formulate
the best possible bounds for this average length and for the maximum length of the period of the
continued fraction expansion of $\sqrt n$, with $[\sqrt n]=k.$
   

PAPERS: mariusjp.tex   mariusjp.pdf

PROGRAMS: special_graphics.c  myprogram.c  graphics.c  former_graphics.c  former_graphics2.c

INVESTIGATOR: Alexandra Gliga

PAPERS: alexajp.tex   alexajp.dvi   alexajp.pdf

PROGRAMS: agprogram.nb