Compound Quadratic Surd Form $\sqrt{a \pm \sqrt{b}}$

2009 ◽  
pp. 7-12
Keyword(s):  
Quadratic Surd

scholarly journals Application of Wynn's epsilon algorithm to periodic continued fractions

1987 ◽  
Vol 30 (2) ◽  
pp. 295-299 ◽  
Author(s):  
M. J. Jamieson
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Rational Numbers ◽  
Quadratic Surd ◽  
Partial Quotients ◽  
Infinite Continued Fraction ◽  
Image Position ◽  
Epsilon Algorithm ◽  
Periodic Continued Fractions

The infinite continued fractionin whichis periodic with period l and is equal to a quadratic surd if and only if the partial quotients, ak, are integers or rational numbers [1]. We shall also assume that they are positive. The transformation discussed below applies only to pure periodic fractions where n is zero.

scholarly journals The Calkin–Wilf Tree of a Quadratic Surd

2019 ◽  
Vol 126 (9) ◽  
pp. 771-785
Author(s):  
Lionel Ponton
Keyword(s):  
Quadratic Surd

scholarly journals ON THE OPTIMAL CONTINUED FRACTION EXPANSION OF A QUADRATIC SURD

2012 ◽  
Vol 93 (1-2) ◽  
pp. 133-156
Author(s):  
KEITH R. MATTHEWS
Keyword(s):  
Continued Fraction ◽  
Continued Fraction Expansion ◽  
Quadratic Surd

AbstractWe describe the period structure of the optimal continued fraction expansion of a quadratic surd, in terms of the period of its nearest square continued fraction expansion. The analysis results in a faster algorithm for determining the optimal continued fraction expansion of a quadratic surd.

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