Abstract
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.
Original language | English |
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Pages (from-to) | 53-76 |
Journal | Journal of the Australian Mathematical Society |
Volume | 93 |
Issue number | 1/2 |
DOIs | |
Publication status | Published - Oct 2012 |
Citation
Cheng, 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.Keywords
- Continued fraction expansion
- Period length
- Schinzel sleeper