quadratic surd Latest Research Papers

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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Period-length equality for the nearest integer and nearest square continued fraction expansions of a quadratic surd

Glasnik Matematicki ◽

10.3336/gm.46.2.01 ◽

2011 ◽

Vol 46 (2) ◽

pp. 269-282 ◽

Cited By ~ 1

Author(s):

Keith R. Matthews ◽

John P. Robertson

Keyword(s):

Continued Fraction ◽

Period Length ◽

Quadratic Surd ◽

Continued Fraction Expansions

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Symmetries of quadratic form classes and of quadratic surd continued fractions. Part II: Classification of the periods’ palindromes

Bulletin of the Brazilian Mathematical Society New Series ◽

10.1007/s00574-010-0005-0 ◽

2010 ◽

Vol 41 (1) ◽

pp. 83-124 ◽

Cited By ~ 2

Author(s):

Francesca Aicardi

Keyword(s):

Quadratic Form ◽

Continued Fractions ◽

Quadratic Surd

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

Lecture Notes on Mathematical Olympiad Courses - Mathematical Olympiad Series ◽

10.1142/9789814293570_0002 ◽

2009 ◽

pp. 7-12

Keyword(s):

Quadratic Surd

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Quadratic Surd Expressions and Their Operations

Lecture Notes on Mathematical Olympiad Courses - Mathematical Olympiad Series ◽

10.1142/9789814293570_0001 ◽

2009 ◽

pp. 1-6

Keyword(s):

Quadratic Surd

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Symmetries of quadratic form classes and of quadratic surd continued fractions. Part I: A Poincaré tiling of the de Sitter world

Bulletin of the Brazilian Mathematical Society New Series ◽

10.1007/s00574-009-0014-z ◽

2009 ◽

Vol 40 (3) ◽

pp. 301-340 ◽

Cited By ~ 2

Author(s):

Francesca Aicardi

Keyword(s):

Quadratic Form ◽

Continued Fractions ◽

De Sitter ◽

Quadratic Surd

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Application of Wynn's epsilon algorithm to periodic continued fractions

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500028352 ◽

1987 ◽

Vol 30 (2) ◽

pp. 295-299 ◽

Cited By ~ 1

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.

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