Download or read book Golden Non euclidean Geometry The Hilbert s Fourth Problem Golden Dynamical Systems And The Fine structure Constant written by Alexey Stakhov and published by World Scientific. This book was released on 2016-07-14 with total page 307 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.See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math
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.
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.
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:
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.
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.
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.
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 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non Euclidean Geometry written by Henry Parker Manning and published by . This book was released on 1901 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Non Euclidean Geometry written by EISENREICH and published by Elsevier. This book was released on 2014-06-28 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Non Euclidean Geometry written by Harold Eichholtz Wolfe and published by . This book was released on 1966 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Elements of Non euclidean Geometry written by D. M. Y. Sommerville and published by . This book was released on 1958 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Euclidean and Non Euclidean Geometry written by Patrick J. Ryan and published by Cambridge University Press. This book was released on 1986-06-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Golden Section and Non Euclidean Geometry in Science and Art written by Oleg Bodnar and published by LAP Lambert Academic Publishing. This book was released on 2015-08-21 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers new sensational information on the realization of rules of the geometry of Minkovskiy in nature. It has been done for the first time after Herman Minkovskiy published his geometrical interpretation of the special theory of relativity one hundred years ago. The author investigates its realization in nature, namely in the growth mechanism of spiro-symmetrical (the so called phylotaxis) plant forms. A detailed mathematical decoding of this mechanism unexpectedly reveals the involvement of golden section - a magic number, with which the history of science and art have always associated the idea of harmony and perfection. The book contains historical information on the development of geometric ideas in science and art, on the evolution of spatial conceptions, their peculiarities and their role in the scientific outlook of the 20th century. The process of the change of spatial conception and, accordingly, of methodological approaches in the architecture and design of the 20th century are regarded from special "geometric" positions.
Download or read book The Non Euclidean Hyperbolic Plane written by P. Kelly and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli dean geometry with some mastery.
Download or read book The Foundations of Geometry and the Non Euclidean Plane written by G.E. Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.
Download or read book Euclidean and Non Euclidean Geometries written by Marvin J. Greenberg and published by Macmillan. This book was released on 1993-07-15 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context. Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres.
