The “golden” hyperbolic models of Universe

Abstract This article presents a review of new mathematical models of the hyperbolic space. These models are based on the golden section. In this article, the authors discuss the hyperbolic Fibonacci and Lucas functions and the surface of the golden shofar, which are the most important of these models. The authors also introduce, within this article, the golden hyperbolic approach for modeling the universe.

[1]  A. Stakhov,et al.  The Golden Shofar , 2005 .

[2]  M. E. Naschie,et al.  Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics , 2006 .

[3]  A. Stakhov.  Fundamentals of a new kind of mathematics based on the Golden Section , 2006 .

[4]  Alexey Stakhov.  Brousentsov's Ternary Principle, Bergman's Number System and Ternary Mirror-symmetrical Arithmetic , 2002, Comput. J..

[5]  R. Mauldin,et al.  Random recursive constructions: asymptotic geometric and topological properties , 1986 .

[6]  Christian Bluhm.  Random recursive construction of Salem sets , 1996 .

[7]  Alexey Stakhov,et al.  The Golden Section and Modern Harmony Mathematics , 1998 .

[8]  M. Naschie.  Quantum mechanics and the possibility of a Cantorian space-time , 1991 .

[9]  Alexey Stakhov,et al.  Algorithmic Measurement Theory , 2009 .

[10]  S. Vajda.  Fibonacci and Lucas Numbers and the Golden Section , 1989 .

[11]  V. Hoggatt.  Fibonacci and Lucas Numbers , 2020, Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science.

[12]  Alexey Stakhov,et al.  Theory of Binet formulas for Fibonacci and Lucas p-numbers , 2006 .

[13]  Alexey Stakhov.  Hyperbolic Fibonacci and Lucas Functions , 2009 .

[14]  A. Stakhov.  Codes of the Golden Proportion , 2009 .

[15]  Hyperbolic universes with a horned topology and the cosmic microwave background anisotropy , 2004, astro-ph/0403597.

[16]  Alexey Stakhov,et al.  The continuous functions for the Fibonacci and Lucas p-numbers , 2006 .

[17]  Alexey Stakhov,et al.  The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering , 2005 .

[18]  A. Stakhov,et al.  The “golden” algebraic equations , 2006 .

[19]  M. Naschie.  Is quantum space a random cantor set with a golden mean dimension at the core , 1994 .

[20]  M. Naschie.  On dimensions of Cantor set related systems , 1993 .

[21]  Alexey Stakhov,et al.  On a new class of hyperbolic functions , 2005 .

[22]  Alexey Stakhov,et al.  The golden section in the measurement theory , 1989 .

[23]  A. Stakhov.  Generalized golden sections and a new approach to the geometric definition of a number , 2004 .