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. Copyright © 2013 Australian Mathematical Publishing Association Inc.
CitationCheng, K. H. F., Guy, R. K., Scheidler, R., & Williams, H. C. (2012). Classification and symmetries of a family of continued fractions with bounded period length. Journal of the Australian Mathematical Society, 93(1/2), 53-76.
- Continued fraction expansion
- Period length
- Schinzel sleeper