An upper bound for the period length of a quadratic irrational

2007 ◽  
Vol 77 (1) ◽  
pp. 129-136 ◽  
Author(s):  
A. Pohl
Keyword(s):  
Upper Bound ◽  
Period Length ◽  
Quadratic Irrational

scholarly journals CLASSIFICATION AND SYMMETRIES OF A FAMILY OF CONTINUED FRACTIONS WITH BOUNDED PERIOD LENGTH

2012 ◽  
Vol 93 (1-2) ◽  
pp. 53-76
Author(s):  
K. H. F. CHENG ◽  
R. K. GUY ◽  
R. SCHEIDLER ◽  
H. C. WILLIAMS
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Period Length ◽  
Continued Fraction Expansion ◽  
Quadratic Irrational ◽  
Continued Fraction Expansions

AbstractIt 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.

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