The Golden Non Euclidean Geometry

Author : Alexey Stakhov
Publisher : World Scientific
ISBN 13 : 9814678317
Total Pages : 308 pages
Book Rating : 4.15/5 ( download)

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Download or read book The “Golden” Non-Euclidean Geometry written by Alexey Stakhov and published by World Scientific. This book was released on 2016-07-14 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Multiverse 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.

Author : Alekseĭ Petrovich Stakhov
Publisher :
ISBN 13 : 9789814678308
Total Pages : 284 pages
Book Rating : 4.09/5 ( download)

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Download or read book The "golden" Non-Euclidean Geometry written by Alekseĭ Petrovich Stakhov and published by . This book was released on 2017 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Boris A. Rosenfeld
Publisher : Springer Science & Business Media
ISBN 13 : 1441986804
Total Pages : 481 pages
Book Rating : 4.01/5 ( download)

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Download or read book A History of Non-Euclidean Geometry written by Boris A. Rosenfeld and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alexey Stakhov
Publisher : World Scientific
ISBN 13 : 9812775838
Total Pages : 745 pages
Book Rating : 4.32/5 ( download)

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Download or read book The Mathematics of Harmony written by Alexey Stakhov and published by World Scientific. This book was released on 2009 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."

Author : Henry Parker Manning
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.85/5 ( download)

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Download or read book Non-Euclidean Geometry written by Henry Parker Manning and published by . This book was released on 1901 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Roberto Bonola
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.09/5 ( download)

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Download or read book Non-Euclidean Geometry written by Roberto Bonola and published by . This book was released on 1912 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines various attempts to prove Euclid's parallel postulate -- by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky.

Author : H. S. M. Coxeter
Publisher : Cambridge University Press
ISBN 13 : 9780883855225
Total Pages : 362 pages
Book Rating : 4.24/5 ( download)

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Download or read book Non-Euclidean Geometry written by H. S. M. Coxeter and published by Cambridge University Press. This book was released on 1998-09-17 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases. This is essential reading for anybody with an interest in geometry.

Author : Duncan M'Laren Young Sommerville
Publisher :
ISBN 13 :
Total Pages : 291 pages
Book Rating : 4.01/5 ( download)

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Download or read book The Elements of Non-Euclidean Geometry written by Duncan M'Laren Young Sommerville and published by . This book was released on 1914 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Julian Lowell Coolidge
Publisher :
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.25/5 ( download)

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Download or read book The Elements of Non-Euclidean Geometry written by Julian Lowell Coolidge and published by . This book was released on 1909 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Stefan Kulczycki
Publisher : Courier Corporation
ISBN 13 : 0486155013
Total Pages : 210 pages
Book Rating : 4.12/5 ( download)

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Download or read book Non-Euclidean Geometry written by Stefan Kulczycki and published by Courier Corporation. This book was released on 2012-07-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible approach features stereometric and planimetric proofs, and elementary proofs employing only the simplest properties of the plane. A short history of geometry precedes the systematic exposition. 1961 edition.