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**Synopsis:** 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.

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.

**From the Inside Flap:**
This unique book overturns our ideas about non-Euclidean geometry and explains the role of the "golden ratio" in Euclid's Elements. It highlights a new view on Euclid's Elements and the history of mathematics based on Proclus' hypothesis. It describes a general theory of "recursive" hyperbolic functions based on the "golden," "silver," and other "metallic" proportions. The book contains an original solution of Hilbert's Fourth Problem for hyperbolic and spherical geometries, and puts forward a problem searching for new hyperbolic and spherical worlds of nature based on this solution. For the first time, the book describes the "golden" qualitative theory of dynamical systems based on the mathematics of harmony. It is intended for a wide range of readers, who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems and dynamical systems.

Title: **(Hardcover)**

Book Condition: **New**

Published by
World Scientific Publishing Co Pte Ltd, Singapore
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Hardcover
Quantity Available: 10

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**Book Description **World Scientific Publishing Co Pte Ltd, Singapore, 2016. Hardback. Condition: New. Language: English . Brand New Book. 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. Seller Inventory # AAC9789814678292

Published by
World Scientific Pub Co Inc
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Quantity Available: > 20

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Rating

**Book Description **World Scientific Pub Co Inc, 2016. HRD. Condition: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Seller Inventory # IB-9789814678292

Published by
World Scientific Publishing Co Pte Ltd

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Hardcover
Quantity Available: 2

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**Book Description **World Scientific Publishing Co Pte Ltd. Hardback. Condition: new. BRAND NEW, The "Golden" Non-Euclidean Geometry: Recursive "Self-Similar" Hyperbolic Functions, Hilbert's Fourth Problem, and "Golden" Dynamical Systems, Alexey Stakhov, Samuil Aranson, This unique book overturns our ideas about non-Euclidean geometry and explains the role of the "golden ratio" in Euclid's Elements. It highlights a new view on Euclid's Elements and the history of mathematics based on Proclus' hypothesis. It describes a general theory of "recursive" hyperbolic functions based on the "golden," "silver," and other "metallic" proportions. The book contains an original solution of Hilbert's Fourth Problem for hyperbolic and spherical geometries, and puts forward a problem searching for new hyperbolic and spherical worlds of nature based on this solution. For the first time, the book describes the "golden" qualitative theory of dynamical systems based on the mathematics of harmony. It is intended for a wide range of readers, who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems and dynamical systems. Seller Inventory # B9789814678292

Published by
World Scientific Publishing Co Pte Ltd, Singapore
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **World Scientific Publishing Co Pte Ltd, Singapore, 2016. Hardback. Condition: New. Language: English . Brand New Book. 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. Seller Inventory # AAC9789814678292

Published by
World Scientific Publishing Co Pte Ltd
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Quantity Available: > 20

Seller:

Rating

**Book Description **World Scientific Publishing Co Pte Ltd, 2016. HRD. Condition: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Seller Inventory # IB-9789814678292

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Quantity Available: 5

Seller:

Rating

**Book Description **Condition: New. Seller Inventory # 24549266-n

Published by
World Scientific Publishing Co Pte Ltd 2016-10-11
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Hardcover
Quantity Available: 5

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**Book Description **World Scientific Publishing Co Pte Ltd 2016-10-11, 2016. Hardcover. Condition: New. Seller Inventory # NU-MAR-00040821

Published by
World Scientific Publishing Co
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

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Hardcover
Quantity Available: > 20

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**Book Description **World Scientific Publishing Co, 2016. Hardcover. Condition: New. Never used!. Seller Inventory # 9814678295

Published by
World Scientific 2016-07-15, New Jersey
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

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Hardcover
Quantity Available: > 20

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**Book Description **World Scientific 2016-07-15, New Jersey, 2016. hardback. Condition: New. Seller Inventory # 9789814678292

Published by
World Scientific Pub Co Inc
(2016)

ISBN 10: 9814678295
ISBN 13: 9789814678292

New
Hardcover
Quantity Available: 2

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**Book Description **World Scientific Pub Co Inc, 2016. Hardcover. Condition: Brand New. 284 pages. 9.25x6.25x1.00 inches. In Stock. Seller Inventory # x-9814678295