The "golden" non-Euclidean geometry : Hilbert's fourth problem, "golden" dynamical systems, and the fine-structure constant
著者
書誌事項
The "golden" non-Euclidean geometry : Hilbert's fourth problem, "golden" dynamical systems, and the fine-structure constant
（Series on analysis, applications and computation, v. 7）
World Scientific, c2017
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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
目次
- Proclus' Hypothesis and Euclid's Elements
- "Golden" Hyperbolic Fibonacci and Lucas Functions and Bodnar's Geometry of Phyllotaxis
- The Mathematics of Harmony and General Theory of the Recursive Hyperbolic Functions Based on the "Golden," "Silver" and other "Metallic" Proportions
- Hyperbolic and Spherical Solution of Hilbert's Fourth Problem: The Way to the Recursive and "Self-Similar" Non-Euclidean Geometries
- The "Golden" Qualitative Theory of Dynamical Systems Based on the Mathematics of Harmony
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