The Golden Non Euclidean Geometry

Author : Alexey Stakhov,Samuil Aranson
Publisher : World Scientific
Page : 308 pages
File Size : 51,9 Mb
Release : 2016-07-14
Category : Mathematics
ISBN : 9789814678315

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The “Golden” Non-Euclidean Geometry by Alexey Stakhov,Samuil Aranson Pdf

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,S. Kh Aranson,Scott Anthony Olsen
Publisher : Unknown
Page : 284 pages
File Size : 50,5 Mb
Release : 2017
Category : Geometry, Non-Euclidean
ISBN : 9814678309

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The "golden" Non-Euclidean Geometry by Alekseĭ Petrovich Stakhov,S. Kh Aranson,Scott Anthony Olsen Pdf

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
Page : 481 pages
File Size : 42,7 Mb
Release : 2012-09-08
Category : Mathematics
ISBN : 9781441986801

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A History of Non-Euclidean Geometry by Boris A. Rosenfeld Pdf

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 : Roberto Bonola
Publisher : Courier Corporation
Page : 452 pages
File Size : 46,6 Mb
Release : 2012-08-15
Category : Mathematics
ISBN : 9780486155036

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Non-Euclidean Geometry by Roberto Bonola Pdf

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 : H. S. M. Coxeter
Publisher : Cambridge University Press
Page : 362 pages
File Size : 50,9 Mb
Release : 1998-09-17
Category : Mathematics
ISBN : 0883855224

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Non-Euclidean Geometry by H. S. M. Coxeter Pdf

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 : Alexey Stakhov
Publisher : World Scientific
Page : 745 pages
File Size : 47,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812775832

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The Mathematics of Harmony by Alexey Stakhov Pdf

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 : EISENREICH
Publisher : Elsevier
Page : 287 pages
File Size : 42,5 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483295312

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Introduction to Non-Euclidean Geometry by EISENREICH Pdf

An Introduction to Non-Euclidean Geometry covers some introductory topics related to non-Euclidian geometry, including hyperbolic and elliptic geometries. This book is organized into three parts encompassing eight chapters. The first part provides mathematical proofs of Euclid’s fifth postulate concerning the extent of a straight line and the theory of parallels. The second part describes some problems in hyperbolic geometry, such as cases of parallels with and without a common perpendicular. This part also deals with horocycles and triangle relations. The third part examines single and double elliptic geometries. This book will be of great value to mathematics, liberal arts, and philosophy major students.

Author : Harold Eichholtz Wolfe
Publisher : Unknown
Page : 346 pages
File Size : 46,7 Mb
Release : 1966
Category : Geometry, Non-Euclidean
ISBN : UVA:X001468900

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Introduction to Non-Euclidean Geometry by Harold Eichholtz Wolfe Pdf

Author : Henry Parker Manning
Publisher : Prabhat Prakashan
Page : 95 pages
File Size : 42,9 Mb
Release : 2021-01-19
Category : Mathematics
ISBN : EAN:6235989716114

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Non-Euclidean Geometry by Henry Parker Manning Pdf

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 : D. M.Y. Sommerville
Publisher : Courier Corporation
Page : 290 pages
File Size : 49,9 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486154589

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The Elements of Non-Euclidean Geometry by D. M.Y. Sommerville Pdf

Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.

Author : I.M. Yaglom
Publisher : Springer
Page : 338 pages
File Size : 41,7 Mb
Release : 1979-02-28
Category : Gardening
ISBN : UOM:39015017136782

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A Simple Non-Euclidean Geometry and Its Physical Basis by I.M. Yaglom Pdf

There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.

Author : ROBERTO. BONOLA
Publisher : Unknown
Page : 0 pages
File Size : 54,9 Mb
Release : 2018
Category : Electronic
ISBN : 1033294500

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NON-EUCLIDEAN GEOMETRY by ROBERTO. BONOLA Pdf

Author : Patrick J. Ryan
Publisher : Cambridge University Press
Page : 240 pages
File Size : 43,7 Mb
Release : 1986-06-27
Category : Mathematics
ISBN : 0521276357

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Euclidean and Non-Euclidean Geometry by Patrick J. Ryan Pdf

A thorough analysis of the fundamentals of plane geometry The reader is provided with an abundance of geometrical facts such as the classical results of plane Euclidean and non-Euclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition, trigonometrical formulas, etc.

Author : Boris A. Rosenfeld
Publisher : Springer
Page : 471 pages
File Size : 51,8 Mb
Release : 1988-09-07
Category : Mathematics
ISBN : 0387964584

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A History of Non-Euclidean Geometry by Boris A. Rosenfeld Pdf

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
Page : 244 pages
File Size : 50,9 Mb
Release : 2020-09-03
Category : Mathematics
ISBN : 9789811213519

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Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences by Alexey Stakhov Pdf

Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' 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 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction 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 generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are 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.