A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics

David F. Haight

doi:doi:10.11648/j.pamj.20150404.11

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A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics

David F. Haight

Received: 4 May 2015 Accepted: 18 May 2015 Published: 16 June 2015

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Abstract

When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.

DOI	10.11648/j.pamj.20150404.11
Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 4, August 2015)
Page(s)	139-146
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fibonacci Sequence, Lucas Sequence, Golden Proportion, “Prime” Prime Number, Hydrogen Fine Structure, The Physical Constants, Binary Computer Code, A Uni-Phi-ed Theory of Mathematics

References

[1]	John Barrow, The Constants, New York, NY: Pantheon, 2002.
[2]	Marcus Chown, “Go figure. Why should nature have a favourite number?” New Scientist, Dec. 21/28, 2002.
[3]	Radu Coldea, et al., “Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry,” Science, Jan. 8 2010. (“Public release: Golden ratio discovered in quantum world. Hidden symmetry observed for the first time in solid state matter: http://www.eurekalert.org/pub_releases/ 2010-01/haog-grd0010510.php)”
[4]	Tobias Dantzig, Number, The Language of Science, fourth edition, New York, NY: the Free Press, 1954.
[5]	Richard Feynman, QED, The Strange Theory of Light and Matter, Princeton, NJ: Princeton University Press, 1985.
[6]	Carlos Figueroa, G. Julio Campos, A. Lamberto Castro, “Study of prime numbers through their historical development applying matlab,” International Journal of Development Research, 2014, vol. 4, no. 12.
[7]	David F. Haight, “Summa Characteristica and the Riemann Hypothesis: scaling Riemann's mountain,” the Journal of Interdisciplinary Mathematics, vol. 11, no. 6, Dec. 2008. (Reprinted online by Taylor and Francis Publishing Group, May 2013.)
[8]	David F. Haight, “Generalizing Riemann: from the L-Functions to the Birch/Swinnerton-Dyer conjecture,” the Journal of Interdisciplinary Mathematics, vol. 13, no. 5, Oct 2010. (Republished online by Taylor and Francis Group, May 2013.)
[9]	H. E. Huntley, The Divine Proportion, New York, NY: Dover Publications, Inc., 1970.
[10]	Gottfried Wilhelm Leibniz, Monadology and other Philosophical Writings, ed. R. Latta, Oxford: Oxford University press, 1965.
[11]	Leibniz, Philosophical Writings, ed. G. H. R. Parkinson, London: Everyman's Library, 1983.
[12]	Leibniz, Selections, ed. P. Wiener, New York, NY: Charles Scribner's Sons, 1951.
[13]	Roger Penrose, The Road to Reality, New York, NY: Alfred A. Knopf, 2004.
[14]	Y. Shang, “A result concerning the ratio of consecutive prime numbers,” Mathematical Sciences Letters, 2013, vol. 2, no. 3.

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APA Style

David F. Haight. (2015). A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics. Pure and Applied Mathematics Journal, 4(4), 139-146. https://doi.org/10.11648/j.pamj.20150404.11

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David F. Haight. A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics. Pure Appl. Math. J. 2015, 4(4), 139-146. doi: 10.11648/j.pamj.20150404.11

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AMA Style

David F. Haight. A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics. Pure Appl Math J. 2015;4(4):139-146. doi: 10.11648/j.pamj.20150404.11

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@article{10.11648/j.pamj.20150404.11,
  author = {David F. Haight},
  title = {A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {4},
  pages = {139-146},
  doi = {10.11648/j.pamj.20150404.11},
  url = {https://doi.org/10.11648/j.pamj.20150404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150404.11},
  abstract = {When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.},
 year = {2015}
}

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TY  - JOUR
T1  - A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics
AU  - David F. Haight
Y1  - 2015/06/16
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150404.11
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AB  - When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.
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Author Information

David F. Haight

Department of History and Philosophy, Plymouth State University, Plymouth, New Hampshire, USA

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APA Style

David F. Haight. (2015). A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics. Pure and Applied Mathematics Journal, 4(4), 139-146. https://doi.org/10.11648/j.pamj.20150404.11

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ACS Style

David F. Haight. A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics. Pure Appl. Math. J. 2015, 4(4), 139-146. doi: 10.11648/j.pamj.20150404.11

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AMA Style

David F. Haight. A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics. Pure Appl Math J. 2015;4(4):139-146. doi: 10.11648/j.pamj.20150404.11

Copy | Download

@article{10.11648/j.pamj.20150404.11,
  author = {David F. Haight},
  title = {A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {4},
  pages = {139-146},
  doi = {10.11648/j.pamj.20150404.11},
  url = {https://doi.org/10.11648/j.pamj.20150404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150404.11},
  abstract = {When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.},
 year = {2015}
}

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TY  - JOUR
T1  - A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics
AU  - David F. Haight
Y1  - 2015/06/16
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150404.11
DO  - 10.11648/j.pamj.20150404.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 139
EP  - 146
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150404.11
AB  - When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.
VL  - 4
IS  - 4
ER  -

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