From Fibonacci Sequence to the Golden Ratio
Joint Authors
Vincenzi, Giovanni
Fiorenza, Alberto
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-3, 3 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-18
Country of Publication
Egypt
No. of Pages
3
Main Subjects
Abstract EN
We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci sequence, and we give an explanation of this property in the framework of the Difference Equations Theory.
We show that the Golden ratio coincides with this limit not because it is the root with maximum modulus and multiplicity of the characteristic polynomial, but, from a more general point of view, because it is the root with maximum modulus and multiplicity of a restricted set of roots, which in this special case coincides with the two roots of the characteristic polynomial.
This new perspective is the heart of the characterization of the limit of ratio of consecutive terms of all linear homogeneous recurrences with constant coefficients, without any assumption on the roots of the characteristic polynomial, which may be, in particular, also complex and not real.
American Psychological Association (APA)
Fiorenza, Alberto& Vincenzi, Giovanni. 2013. From Fibonacci Sequence to the Golden Ratio. Journal of Mathematics،Vol. 2013, no. 2013, pp.1-3.
https://search.emarefa.net/detail/BIM-454267
Modern Language Association (MLA)
Fiorenza, Alberto& Vincenzi, Giovanni. From Fibonacci Sequence to the Golden Ratio. Journal of Mathematics No. 2013 (2013), pp.1-3.
https://search.emarefa.net/detail/BIM-454267
American Medical Association (AMA)
Fiorenza, Alberto& Vincenzi, Giovanni. From Fibonacci Sequence to the Golden Ratio. Journal of Mathematics. 2013. Vol. 2013, no. 2013, pp.1-3.
https://search.emarefa.net/detail/BIM-454267
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-454267