Classification and Symmetries of a Family of Continued Fractions with Bounded Period Length
نویسندگان
چکیده
It is well known that the regular continued fraction expansion of a quadratic irrational is symmetric about its centre; we refer to this symmetry as horizontal. However, an additional vertical symmetry is exhibited by the continued fraction expansions arising from a family of quadratics known as Schinzel sleepers. This paper provides a method for generating every Schinzel sleeper and investigates their period lengths as well as both their horizontal and vertical symmetries. 2010 Mathematics subject classification: primary 11A55; secondary 11Y65.
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