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“Golden” Fibonacci Goniometry, Fibonacci-Lorentz Transformations, and Hilbert's Fourth Problem
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“Golden” Fibonacci Goniometry, Fibonacci-Lorentz Transformations, and Hilbert’s Fourth Problem

(the article was published in «Congressuss Numerantium, Vol. CXCIII, Dec. 2008 )


This study is devoted to the development of the “golden” Fibonacci goniometry and new approach to Lorentz transformations, which are used in Einstein's special theory of relativity. We propose Fibonacci-Lorentz transformations, which are based on the "golden" Fibonacci goniometry and symmetric hyperbolic Fibonacci functions which in turn are based on the golden mean - the world’s oldest scientific paradigm of harmony and beauty. We obtain a cosmological interpretation of change at the velocity light before, at the moment of, and following the bifurcation, known as the Big Bang.  The article also presents the authors’ results on the creation of an infinite set of isometric models of Lobachevski’s plane, which are based on the use of the hyperbolic Fibonacci -functions, where  is any real number, in particular, symmetric hyperbolic Fibonacci functions with, which is directly relevant to the Hilbert’s  Fourth Problem.


Alexey Stakhov, Samuil Aranson


Full article in Word format (1.18 Mb)

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