This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of "recursive" hyperbolic functions based on the "Mathematics of Harmony," and the "golden," "silver," and other "metallic" proportions. Then, these theories are used to derive an original solution to Hilbert's Fourth Problem for hyperbolic and spherical geometries. On this journey, the book describes the "golden" qualitative theory of dynamical systems based on "metallic" proportions. Finally, it presents a solution to a Millennium Problem by developing the Fibonacci special theory of relativity as an original physical-mathematical solution for the fine-structure constant. It is intended for a wide audience who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems, dynamical systems, and Millennium Problems.
See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math
The Golden Ratio, Fibonacci Numbers, and the "Golden" Hyperbolic Fibonacci and Lucas Functions
The Mathematics of Harmony and General Theory of Recursive Hyperbolic Functions
Hyperbolic and Spherical Solutions of Hilbert's Fourth Problem: The Way to the Recursive Non-Euclidean Geometries
Introduction to the "Golden" Qualitative Theory of Dynamical Systems Based on the Mathematics of Harmony
The Basic Stages of the Mathematical Solution to the Fine-Structure Constant Problem as a Physical Millennium Problem
Appendix: From the "Golden" Geometry to the Multiverse
Readership: Advanced undergraduate and graduate students in mathematics and theoretical physics, mathematicians and scientists of different specializations interested in history of mathematics and new mathematical ideas.
The book develops many unexpected ideas concerning the history of mathematics, in particular, a new view on Euclid's Elements, based on Proclus' hypothesis
A general theory of the "recursive" hyperbolic functions based on the "golden", "silver" and other "metallic" proportions underlies the present book
New approaches to the solution of Hilbert's Fourth Problem as a candidate on the Millennium Problem in geometry follow from this theory
New and interesting results in the field of qualitative dynamical systems based on the mathematics of harmony are discussed
Original solution to the problem of fine-structure constant as a physical Millennium Problem
All these mathematical results have great value for a wide range of mathematicians and specialists in theoretical physics