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Consecutive FIBONACCI-number ratios F(n+1) / F(n) as a damped alternating oscillator around and approximating Phi = Φ

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Consecutive FIBONACCI-number ratios F(n+1) / F(n) as a damped alternating oscillator around and approximating Phi = Φ by Stefan Geier Because of lim (Fn/Ln) for n to infinite and Fn the n-th FIBONACCI-number and Ln the n-th LUCAS-number the content of GEIER Stefan et al. “Consecutive Lucas-number ratios L(n+1) / L(n) as a damped alternating oscillator around and approximating Phi = Φ“ is correct for FIBONACCI-numbers, too. Therefore we state: Consecutive FIBONACCI-number ratios F(n+1) / F(n) can be interpreted as a damped alternating oscillator around and approximating Phi = Φ . Critique welcome! Refinement welcome! Yours sincerely, Stefan Geier Gerhart-Hauptmann-Straße 6 83071 Stephanskirchen, Haidholzen, Germany, Europe References: Chandra, Pravin and Weisstein, Eric W. "Fibonacci Number." From MathWorld --A Wolfram Resource. https://mathworld.wolfram.com/FibonacciNumber.html . Geier Stefan et al. Consecutive Lucas-number ratios L(n+1) / L(n) as a damped...

Hox Genes Fit FIBONACCI-Numbers and LUCAS-Numbers to a Very Reasonable Extent by Stefan Geier

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Hox Genes Fit FIBONACCI-Numbers and LUCAS-Numbers to a Very Reasonable Extent by Stefan Geier Hypothesis: Hox genes fit FIBONACCI-Numbers and LUCAS-Numbers. Evidence: 1. Number of Hox genes: 1.1. The typical number of Hox genes in mammals is13; 13 is the 7th FIBONACCI-number F(7). 1.2. The typical number of Hox genes in zebrafish is 13; 13 is the 7th FIBONACCI-number F(7). 1.3. The typical number of Hox genes in Drosophila is 8; 8 is the 6th FIBONACCI-number F(6). 2. Number of chromosomal clusters (secondary evidence): 2.1. The typical number of chromosomal clusters of Hox genes in mammals is 4; 4 is the third LUCAS-number L(3) . 2.2. The typical number of of chromosomal clusters of Hox genes in zebrafish is 7; 7 is the fourth LUCAS-number L(4). The first Fibonacci-numbers and Lucas-numbers: Fibonacci F(n ): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... Lucas L(n ): 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ... In addition,  the recognition-helix interval  is framed by 47=L(8) and 55...

A Note on "Hox genes, homeodomain specificity and GEIER's Fibonacci/Lucas-number programme in development (GEIER’s equations and Hox Genes, Part 1)" by Stefan Geier et al.

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A Note on "Hox genes, homeodomain specificity and GEIER's Fibonacci/Lucas-number programme in development (GEIER’s equations and Hox Genes, Part 1)" by Stefan Geier et al.   This paper is a bold and stimulating attempt to connect established Hox biology with a Fibonacci/Lucas-based numerical framework, and it succeeds in doing so without abandoning biological seriousness [1–4]. Its main virtue is conceptual: the authors do not present the numerical observations as settled mechanism, but as a falsifiable research programme that can be assessed through future replication, curation and null-model testing. The biological foundation is strong. The manuscript accurately reflects the current view that Hox genes are central regulators of anterior-posterior patterning and that their activity depends on combinatorial specificity, cofactors, chromatin context and developmental timing. This is an important strength, because it grounds the numerical discussion in a well-established ...

First Look: FIBONACCI-Numbers and LUCAS-Numbers and Andes Virus (Hanta Virus): A Reasonable Fit

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First Look: FIBONACCI-Numbers and LUCAS-Numbers and Andes Virus (Hanta Virus): A Reasonable Fit by Stefan Geier Starting Structure of t he  Andes virus (ANDV) Nucleoprotein (N) N-terminal domain  (residues 1–74) Helix 1  1–35 Forms the initial hydrophobic interface for trimerization. 34 is a FIBONACCI-number F(9) Linker  36–43 Flexible loop connecting the two main helices. 8 is a  FIBONACCI-number  F(6) Helix 2  44–74 Provides the second "arm" of the coiled-coil to stabilize the trimer. 31 - 2 = 29;  29 is a LUCAS-number L(7), difference=2 The experimentally studied ANDV nucleoprotein N-terminal domain is N1–74. 76 is s a LUCAS-number L(9), difference=2. The Heptad Repeats fit L(4)=7**.  The first Fibonacci-numbers and Lucas-numbers: Fibonacci F(n ): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... Lucas L(n ): 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ... The above provides an at least reasonable association of the  Andes virus (ANDV) Nucleo...

FIBONACCI-Numbers, SHOEMAKER-LEVY 9 and Gravitational Tidal Forces: Impact of 21 = F(8) Fragments on Jupiter in 1994: A Corroboration of GEIER's Equations

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"Proposition: The 21 Fragment Count of  SHOEMAKER-LEVY 9 Fragmented Due to Gravitational Tidal Forces Represents the 8th FIBONACCI-Number and Thus Corroborates GEIER's Equations" by Stefan Geier We want to present the following proposition: The 21 fragment count* of the comet SHOEMAKER-LEVY 9 fragmented due to gravitational tidal forces (see ROCHE limit) represents the 8th FIBONACCI-number and thus corroborates GEIER's Equations (to some extent or, however, weak). Falsification and refinement is possible. The first Fibonacci-numbers and Lucas-numbers: Fibonacci F(n ): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... Lucas L(n ): 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ... Yours sincerely, Stefan Geier Gerhart-Hauptmann-Str.6 83071 Haidholzen, Germany (Of course, somehow "very crazy". See: Roger PENROSE, too) References: *Anderson Paul Scott:  Remembering Comet Shoemaker-Levy 9's Impact on Jupiter, 23 Years Ago This Week" . AmericaSpace. July 17, 2017. Geier...

First evidence for a FIBONACCI-number and LUCAS-number structure in mammalian spermatozoa flagellum structure

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First evidence for a FIBONACCI-number and LUCAS-number structure in mammalian spermatozoa flagellum structure by Stefan Geier To uré A (2019) Importance of SLC26 Transmembrane Anion Exchangers in Sperm Post-testicular Maturation and Fertilization Potential. Front. Cell Dev. Biol. 7:230.  doi: 10.3389/fcell.2019.00230  (Wikipedia Commons) Please, have a look at the Fibonacci-number and Lucas-number structure of a) the cross-sectio: LC: 2 = F(3) = L(0) ODF above LC: 3 = F(4) = L(2) ODF below LC: 4 = L(3) b) the midpiece: Mitochondria (left and right): 8 x 2 = F(6) x F(3) or F(6) x L(0) This Fibonacci-number and Lucas-number structure of the flagellum of mammalian spermatoza provides evidence, however weak, for GEIER's equations. The first Fibonacci-numbers and Lucas-numbers: Fibonacci F(n ): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... Lucas L(n ): 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ... Yours sincerely, Stefan Geier Gerhart-Hauptmann-Str.6 83071 Haidholzen, Germany (Of course, ...

Very Crazy Hypothesis: The 9 + x Structure of Sperms Reflects an Evolutionary Adaption to the 9 Space Dimensions (3 NEWTON-EINSTEIN and & 6 CALABI-YAU) of String Theories

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Very Crazy Hypothesis: The 9 + x Structure of Sperms Reflects an Evolutionary Adaption to the 9 Space Dimensions (3 NEWTON-EINSTEIN and & 6 CALABI-YAU) of String Theories such as M-Theory or F-Theory by Stefan Geier We would like to introduce, in the context of GEIER’s equations and GEIER's r(KKCYMF), the hypothesis that most species' 9 + x structure of flagellar segments of sperms (* Fig. 2) reflects an evolutionary adaption to the 9 space dimensions (3 NEWTON-EINSTEIN and & 6 CALABI-YAU) of most string theories such as M-Theory or F-Theory. (x is standing for the brane dimension and the up to 2 additional time dimensions.) Hypothesis:  The 9 + x Structure of F lagellar Segments of Most  Sperms Reflects an Evolutionary Adaption to the 9 Space Dimensions (3 NEWTON-EINSTEIN and & 6 CALABI-YAU) of String Theories such as M-Theory or F-Theory. References: ·  Geier Stefan et al. Sperm cell radii and GEIER's r(KKCYMF): all our literature-derived sperm-cell rad...