Number Theory

   

Creation of an Infinite Fibonacci Number Sequence Table

Authors: Harry K. Hahn

A Fibonacci-Number-Sequences-Table was developed, which contains infinite Fibonacci-Sequences. This was achieved with the help of research results from an extensive botanical study. This study examined the phyllotactic patterns ( Fibonacci-Sequences ) which appear in the tree-species “Pinus mugo“ at different altitudes ( from 550m up to 2500m ) With the increase of altitude above around 2000m the phyllotactic patterns change considerably, the number of patterns ( different Fibonacci Sequences ) grows from 3 to 12, and the relative frequency of the main Fibonacci Sequence decreases from 88 % to 38 %. The appearance of more Fibonacci-Sequences in the plant clearly is linked to environmental ( physical ) factors changing with altitude. Especially changes in temperature- / radiation- conditions seem to be the main cause which defines which Fibonnacci-Patterns appear in which frequency. The developed ( natural ) Fibonacci-Sequence-Table shows interesting spatial dependencies between numbers of different Fibonacci-Sequences, which are connected to each other, by the golden ratio ( constant Phi ) --> see Table An interesting property of the numbers in the main Fibonacci-Sequence F1 seems to be, that these numbers contain all prime numbers as prime factors ! in all other Fibonacci-Sequences ≥ F2, which are not a multiple of Sequence F1, certain prime factors seem to be missing in the factorized Fibbonacci-Numbers ( e.g. in Sequences F2, F6 & F8 ). With the help of another study ( Title: Phase spaces in Special Relativity : Towards eliminating gravitational singularities ) a way was found to express (calculate) all natural numbers and their square roots only by using constant Phi (ϕ) and 1. An algebraic term found by Mr Peter Danenhower, in his study, made this possible. With the formulas which I found, it seems to be possible to eliminate number systems and base mathematics only on Phi (ϕ) and 1 ( see my 12 conjectures )

Comments: 16 pages, 6 figures, 8 tables

Download: PDF

Submission history

[v1] 2020-08-04 20:04:46
[v2] 2020-08-11 19:31:51

Unique-IP document downloads: 332 times

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