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Special Issue "Fibonacci and Lucas Numbers and the Golden Ratio in Physics and Biology"

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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 15 January 2024 | Viewed by 12057

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Dr. Tidjani Negadi

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Guest Editor

Physics Department, Faculty of Exact and Applied Sciences, University of Oran1, Oran, Algeria
Interests: theoretical physics; mathematical biology

Prof. Dr. Michel Planat

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Institut FEMTO-ST, CNRS and Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
Interests: foundations of quantum theory; quantum computation; number theory; graph theory; finite groups and finite geometries; Grothendieck’s dessins d’enfants; quantum statistical physics; quantum brain
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Special Issue Information

Dear Colleagues,

This Special Issue intends to provide a platform for researchers in physics and biology whose work is connected to Fibonacci (and Lucas) numbers and the golden ratio. These concepts of great mathematical simplicity and beauty continue to fascinate scholars in many fields such as quantum physics, general relativity, astronomy, chemistry, biology, and architecture, to name but a few.

In quantum physics, Fibonacci numbers and the related golden ratio have appeared in recent works devoted to nonlinear photonic crystals, quasi-one-dimensional Ising ferromagnetism and non-Abelian anyons of the Fibonacci type. They also occur in atomic physics, quasicrystals, chaos, superconductivity, astrophysics, and black holes. In biology, the golden ratio was found to appear in several works about the human body, plant phyllotaxis, DNA nucleotide sequences, the genetic code, and the topology of viruses.

The scope of this Special Issue is large enough to encompass all aspects of research in physics and biology involving the golden ratio and Fibonacci and/or Lucas numbers. We strongly encourage all our interested colleagues to submit details of their latest work.

Dr. Tidjani Negadi
Prof. Dr. Michel Planat
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Fibonacci and Lucas numbers
golden ratio
symmetry
quantum physics
DNA/RNA
mathematical biology
genetic code

Published Papers (4 papers)

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Research

Open AccessArticle

p-Numerical Semigroups of Generalized Fibonacci Triples

Takao Komatsu

Shanta Laishram

and

Pooja Punyani

Symmetry 2023, 15(4), 852; https://doi.org/10.3390/sym15040852 - 03 Apr 2023

Cited by 2 | Viewed by 543

Abstract

For a nonnegative integer p, we give explicit formulas for the p-Frobenius number and the p-genus of generalized Fibonacci numerical semigroups. Here, the p-numerical semigroup

S_{p}

is defined as the set of integers whose nonnegative integral linear combinations [...] Read more.

For a nonnegative integer p, we give explicit formulas for the p-Frobenius number and the p-genus of generalized Fibonacci numerical semigroups. Here, the p-numerical semigroup

S_{p}

is defined as the set of integers whose nonnegative integral linear combinations of given positive integers

a_{1}, a_{2}, \dots, a_{k}

are expressed in more than p ways. When

p = 0

S_{0}

with the 0-Frobenius number and the 0-genus is the original numerical semigroup with the Frobenius number and the genus. In this paper, we consider the p-numerical semigroup involving Jacobsthal polynomials, which include Fibonacci numbers as special cases. We can also deal with the Jacobsthal–Lucas polynomials, including Lucas numbers accordingly. An application on the p-Hilbert series is also provided. There are some interesting connections between Frobenius numbers and geometric and algebraic structures that exhibit symmetry properties. Full article

(This article belongs to the Special Issue Fibonacci and Lucas Numbers and the Golden Ratio in Physics and Biology)

Open AccessArticle

Voronoi Diagrams Generated by the Archimedes Spiral: Fibonacci Numbers, Chirality and Aesthetic Appeal

and

Symmetry 2023, 15(3), 746; https://doi.org/10.3390/sym15030746 - 17 Mar 2023

Viewed by 1268

Abstract

Voronoi mosaics inspired by seed points placed on the Archimedes Spirals are reported. Voronoi (Shannon) entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi tessellations generated by the seeds located on the Archimedes spiral and separated by linearly growing radial distance demonstrate a switch in their chirality. Voronoi mosaics built from cells of equal size, which are of primary importance for the decorative arts, are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant distribution of points when the distance between the seed points is of the same order of magnitude as the distance between the turns of the spiral. Penta- and heptagonal “defected” cells appeared in the Voronoi diagrams due to the finite nature of the pattern. The ordered Voronoi tessellations demonstrating the Voronoi entropy larger than 1.71, reported for the random 2D distribution of points, were revealed. The dependence of the Voronoi entropy on the total number of seed points located on the Archimedes Spirals is reported. Voronoi tessellations generated by the phyllotaxis-inspired patterns are addressed. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed. Full article

(This article belongs to the Special Issue Fibonacci and Lucas Numbers and the Golden Ratio in Physics and Biology)

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Open AccessArticle

The Metallic Ratio of Pulsating Fibonacci Sequences

Kittipong Laipaporn

Kiattiyot Phibul

and

Prathomjit Khachorncharoenkul

Symmetry 2022, 14(6), 1204; https://doi.org/10.3390/sym14061204 - 10 Jun 2022

Cited by 2 | Viewed by 1286

Abstract

The golden ratio and the Fibonacci sequence

(F_{n})

are well known, as is the fact that the ratio

\frac{F_{n + 1}}{F_{n}}

converges to the golden ratio for sufficiently large n. In this paper, we investigate the [...] Read more.

The golden ratio and the Fibonacci sequence

(F_{n})

are well known, as is the fact that the ratio

\frac{F_{n + 1}}{F_{n}}

converges to the golden ratio for sufficiently large n. In this paper, we investigate the metallic ratio—a generalized version of the golden ratio—of pulsating Fibonacci sequences in three forms. Two of these forms are considered in the sense of pulsating recurrence relations, and their diagrams can be represented by symmetry, which is one of their distinguishing characteristics. The third form is the Fibonacci sequence in bipolar quantum linear algebra (BQLA), which also pulsates. Full article

(This article belongs to the Special Issue Fibonacci and Lucas Numbers and the Golden Ratio in Physics and Biology)

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Figure 1

Open AccessArticle

DNA Structure and the Golden Ratio Revisited

Stuart Henry Larsen

Symmetry 2021, 13(10), 1949; https://doi.org/10.3390/sym13101949 - 16 Oct 2021

Cited by 1 | Viewed by 6274

Abstract

B-DNA, the informational molecule for life on earth, appears to contain ratios structured around the irrational number 1.618…, often known as the “golden ratio”. This occurs in the ratio of the length:width of one turn of the helix; the ratio of the spacing of the two helices; and in the axial structure of the molecule which has ten-fold rotational symmetry. That this occurs in the information-carrying molecule for life is unexpected, and suggests the action of some process. What this process might be is unclear, but it is central to any understanding of the formation of DNA, and so life. Full article

(This article belongs to the Special Issue Fibonacci and Lucas Numbers and the Golden Ratio in Physics and Biology)

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Special Issue "Fibonacci and Lucas Numbers and the Golden Ratio in Physics and Biology"

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