"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure ConstantWorld Scientific, 2016 M07 14 - 308 pages 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 |
Contents
Chapter 1 The Golden Ratio Fibonacci Numbers and the Golden Hyperbolic Fibonacci and Lucas Functions | 1 |
Chapter 2 The Mathematics of Harmony and General Theory of Recursive Hyperbolic Functions | 51 |
The Way to the Recursive NonEuclidean Geometries | 89 |
Chapter 4 Introduction to the Golden Qualitative Theory of Dynamical Systems Based on the Mathematics of Harmony | 149 |
Other editions - View all
Common terms and phrases
Academy of Trinitarism accessed November Big Bang billion Bodnar’s geometry cFs(a cFX(a class of hyperbolic classic hyperbolic functions dimensionless dynamical systems Euclid’s Elements Euclidean Fibonacci and Lucas Fibonacci Association Fibonacci numbers Fibonacci special theory Fibonacci speed fine-structure constant foliation Q Free Encyclopedia Gaussian curvature golden ratio Golden Section graph Hilbert’s Fourth Problem hyperbolic Fibonacci hyperbolic functions hyperbolic geometry icosahedron integer irrational foliation irrational number Klein Light Ages light source Lucas functions Lucas hyperbolic functions Lucas numbers Math mathematician Mathematics of Harmony metallic proportions metric form 3.30 Millennium Problem Moscow non-Euclidean geometry parameter phyllotaxis physical Platonic solids Poincaré’s pseudo-sphere real number recurrence relation rotation number Russian sequences singularities solution to Hilbert’s speed of light sphere S2 spherical metric Stakhov surface M2 symmetric Fibonacci theory of relativity tions torus Tº Universe vacuum values Wikipedia X-Fibonacci Φλ