"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant PDF Download
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Author: Alexey Stakhov
Publisher: World Scientific
ISBN: 9814678317
Category : Mathematics
Languages : en
Pages : 307
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Book Description
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
Author: Alexey Stakhov
Publisher: World Scientific
ISBN: 9814678317
Category : Mathematics
Languages : en
Pages : 307
Get Book Here
Book Description
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
Author: Boris A. Rosenfeld
Publisher: Springer Science & Business Media
ISBN: 1441986804
Category : Mathematics
Languages : en
Pages : 481
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Book Description
The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
Author: Harold E. Wolfe
Publisher: Courier Corporation
ISBN: 0486498506
Category : Mathematics
Languages : en
Pages : 274
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Book Description
One of the first college-level texts for elementary courses in non-Euclidean geometry, this volumeis geared toward students familiar with calculus. Topics include the fifth postulate, hyperbolicplane geometry and trigonometry, and elliptic plane geometry and trigonometry. Extensiveappendixes offer background information on Euclidean geometry, and numerous exercisesappear throughout the text.Reprint of the Holt, Rinehart & Winston, Inc., New York, 1945 edition
Author: Henry Parker Manning
Publisher: Prabhat Prakashan
ISBN:
Category : Mathematics
Languages : en
Pages : 95
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Book Description
Non-Euclidean Geometry is now recognized as an important branch of Mathematics. Those who teach Geometry should have some knowledge of this subject; and all who are interested in Mathematics will find much to stimulate them and much for them to enjoy in the novel results and views that it presents. This book is an attempt to give a simple and direct account of the NonEuclidean Geometry; and one which presupposes but little knowledge of Mathematics. The first three chapters assume a knowledge of only Plane and Solid Geometry and Trigonometry; and the entire book can be read by one who has taken the mathematical courses commonly given in our colleges.
Author: Roberto Bonola
Publisher: Courier Corporation
ISBN: 048615503X
Category : Mathematics
Languages : en
Pages : 452
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Book Description
Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs, and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, others. Includes 181 diagrams.
Author: Duncan M'Laren Young Sommerville
Publisher:
ISBN:
Category : Bell's mathematical series for schools and colleges
Languages : en
Pages : 588
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Book Description
Author: Harold Scott Macdonald Coxeter
Publisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 308
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Book Description
Author: Alekseĭ Petrovich Stakhov
Publisher:
ISBN: 9789814678308
Category : Geometry, Non-Euclidean
Languages : en
Pages : 284
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Book Description
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. Contents:The Golden Ratio, Fibonacci Numbers, and the'Golden'Hyperbolic Fibonacci and Lucas FunctionsThe Mathematics of Harmony and General Theory of Recursive Hyperbolic FunctionsHyperbolic and Spherical Solutions of Hilbert's Fourth Problem: The Way to the Recursive Non-Euclidean GeometriesIntroduction to the'Golden'Qualitative Theory of Dynamical Systems Based on the Mathematics of HarmonyThe Basic Stages of the Mathematical Solution to the Fine-Structure Constant Problem as a Physical Millennium ProblemAppendix: From the'Golden'Geometry to the MultiverseReadership: 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.
Author: Julian Lowell Coolidge
Publisher:
ISBN:
Category : Geometry, Non-Euclidean
Languages : en
Pages : 320
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Book Description
Author: H. S. M. Coxeter
Publisher: American Mathematical Soc.
ISBN: 1614445168
Category : Mathematics
Languages : en
Pages : 336
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Book Description
A reissue of Professor Coxeter's classic text on non-euclidean geometry.
