Continued fractions

Borwein, Jonathan M.; Poorten, Alf van der; Shallit, Jeffrey; Zudilin, Wadim

doi:10.1017/cbo9780511902659.003

Cited by 6 publications

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“…However, all of the matrices on the left here have determinant , and thus so does their product. In fact, for any matrix with determinant , the action of the matrix on an irrational number will alter the head of the expansion and leave the tail unchanged (see [BvdPSZ14, Theorem 2.37]), thus preserving CF-normality.…”

Section: Introductionmentioning

confidence: 99%

Non-trivial matrix actions preserve normality for continued fractions

Vandehey¹

2017

Compositio Math.

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Section: Introductionmentioning

confidence: 99%

Non-trivial matrix actions preserve normality for continued fractions

Vandehey¹

2017

Compositio Math.

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“…(see [1], p. 93) one easily obtains e = ⌈3, 4k, 3, 2 (4k−1) ⌉ ∞ k=1 = ⌈3, 4, 3, 2 (3) , 3, 8, 3, 2 (7) , . .…”

Section: Introduction and Resultsmentioning

confidence: 99%

On the asymptotic behavior of Dedekind sums

Girstmair¹

2014

Preprint

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Let z be a real quadratic irrational. We compare the asymptotic behavior of Dedekind sums S(p k , q k ) belonging to convergents p k /q k of the regular continued fraction expansion of z with that of Dedekind sums S(s j /t j ) belonging to convergents s j /t j of the negative regular continued fraction expansion of z. Whereas the three main cases of this behavior are closely related, a more detailed study of the most interesting case (in which the Dedekind sums remain bounded) exhibits some marked differences, since the cluster points depend on the respective periods of these expansions. We show in which cases cluster points of S(s j , t j ) can coincide with cluster points of S(p k , q k ). An important tool for our purpose is a criterion that says which convergents s j /t j of z are convergents p k /q k .

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A Random Walk Through Experimental Mathematics

Chan

Corless

2020

Springer Proceedings in Mathematics &Amp; Statistics

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We describe our adventures in creating a new first-year course in Experimental Mathematics that uses active learning. We used a stateof-the-art facility, called The Western Active Learning Space, and got the students to 'drive the spaceship' (at least a little bit). This paper describes some of our techniques for pedagogy, some of the vignettes of experimental mathematics that we used, and some of the outcomes. EYSC was a student in the simultaneously-taught senior sister course "Open Problems in Experimental Mathematics" the first time it was taught and an unofficial co-instructor the second time. Jon Borwein attended the Project Presentation Day (the second time) and gave thoughtful feedback to each student. This paper is dedicated to his memory.

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Continued fractions

Cited by 6 publications

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Non-trivial matrix actions preserve normality for continued fractions

Non-trivial matrix actions preserve normality for continued fractions

On the asymptotic behavior of Dedekind sums

A Random Walk Through Experimental Mathematics

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