^a International Club of the Golden Section, 6 McCreary Trail, Bolton, ON, Canada L7E2C8
^b International Club of the Golden Section, 3611 Ranch Road, Apt 21-3, Columbia, SC 29206, USA

Abstract

The goal of the present article is to develop the «continues» approach to the recurrent Fibonacci sequence. The main result of the article is new mathematical model of a curve-linear space based on a special second-degree function named «The Golden Shofar».

1. Introduction

As it is well known that the concept of Harmony, which is based on the Golden Section, is one of the most important scientific concepts of ancient science. In the Ancient Greek's philosophy, Harmony was opposed to Chaos and meant the organization of the Universe. The ingenious Russian philosopher Alexey Losev writes: «From Plato's point of view and generally from the view of all antique cosmology, the Universe by itself is the certain proportional whole that subordinates to the law of harmonic division, namely, the Golden Section».

The concepts of Symmetry and Harmony are used widely in modern physical research [1-16]. In the paper [3] written by Mauldin and Willams in 1986 they «proved a theorem which at first sight may seem slightly paradoxical but we perceive as excitingly interesting. This theorem states that the Hausdorf dimension of a randomly constructed Cantor set is where is the Golden Mean» (quotation from [6]). The well-known Russian theoretical physicist Prof.

Vladimirov (Moscow University) finished his book on «Metaphysics» [16] with the following words: «Thus, it is possible to assert that in the theory of electroweak interactions there are relations that approximately coincide with the «Golden Section» that play an important role in the various areas of science and art».

The works of Shechtman, Butusov, Mauldin and William, El Naschie, and Vladimirov show that it is not easily possible to imagine the future progress in physical and cosmological research without the Golden Section.

That is why the development of the new mathematical apparatus based on the Golden Section is an important problem of modern theoretical physics. The present article is continuation of the works [17-19] that were devoted to the theory of the hyperbolic Fibonacci and Lucas functions based on the Golden Section. The main result of the article is a new mathematical model of a curve-linear space based on a special second-degree function named «The Golden Shofar».


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