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Representing Numbers Using Fibonacci Variants

Stephen K. Lucas

in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164038
eISBN:
9781400881338
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164038.003.0017
Subject:
Mathematics, History of Mathematics

This chapter introduces the Zeckendorf representation of a Fibonacci sequence, a form of a natural number which can be easily found using a greedy algorithm: given a number, subtract the largest ... More


The Cookie Monster Problem

Leigh Marie Braswell and Tanya Khovanova

in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164038
eISBN:
9781400881338
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164038.003.0016
Subject:
Mathematics, History of Mathematics

This chapter examines the problem of the “Cookie Monster number.” In 2002, Cookie Monster® appeared in the book The Inquisitive Problem Solver by Vaderlind, Guy, and Larson, where the hungry monster ... More


Quasi-Periodicity and Chaos

Robert C. Hilborn

in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507239
eISBN:
9780191709340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507239.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explores the quasi-periodicity route to chaos in which the behaviour is characterized by two (or more) incommensurate frequencies. Poincare sections, frequency-locking, winding numbers, ... More


Higher-dimensional approach

Walter Steurer and Julia Dshemuchadse

in Intermetallics: Structures, Properties, and Statistics

Published in print:
2016
Published Online:
September 2016
ISBN:
9780198714552
eISBN:
9780191782848
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198714552.003.0004
Subject:
Physics, Crystallography

To understand the structural ordering of aperiodic crystals such as incommensurately modulated phases, composite crystals, quasicrystals and their structurally closely related rational approximants, ... More


Golden Means: Music, Translation and the Patersonnet

Hugh Haughton

in Don Paterson: Contemporary Critical Essays

Published in print:
2014
Published Online:
September 2015
ISBN:
9780748669417
eISBN:
9781474406338
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748669417.003.0002
Subject:
Literature, 20th-century and Contemporary Literature

This chapter explores Paterson's derivations from and implementations of fourteen-line form, in the light of his quasi-mathematical explanations for its ubiquity. Paterson has paid special attention ... More


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