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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
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