The Non Euclidean Revolution
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The Non Euclidean Revolution
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Author : Richard J. Trudeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-08
The Non Euclidean Revolution written by Richard J. Trudeau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-08 with Mathematics categories.
Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.
The Non Euclidean Revolution
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Author : Richard J. Trudeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
The Non Euclidean Revolution written by Richard J. Trudeau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world.
A History Of Non Euclidean Geometry
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Author : Boris A. Rosenfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-08
A History Of Non Euclidean Geometry written by Boris A. Rosenfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-08 with Mathematics categories.
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.
A History Of Non Euclidean Geometry
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Author : Boris A. Rosenfeld
language : en
Publisher: Springer
Release Date : 1988-09-07
A History Of Non Euclidean Geometry written by Boris A. Rosenfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-09-07 with Mathematics categories.
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.
In The Search For Beauty Unravelling Non Euclidean Geometry
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Author : Voldemar Smilga
language : en
Publisher: World Scientific
Release Date : 2018-11-22
In The Search For Beauty Unravelling Non Euclidean Geometry written by Voldemar Smilga and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-22 with Mathematics categories.
This is a popular book that chronicles the historical attempts to prove the fifth postulate of Euclid on parallel lines that led eventually to the creation of non-Euclidean geometry. To absorb the mathematical content of the book, the reader should be familiar with the foundations of Euclidean geometry at the high school level. But besides the mathematics, the book is also devoted to stories about the people, brilliant mathematicians starting from Pythagoras and Euclid and terminating with Gauss, Lobachevsky and Klein. For two thousand years, mathematicians tried to prove the fifth postulate (whose formulation seemed to them too complicated to be a real postulate and not a theorem, hence the title In the Search for Beauty). But in the 19th century, they realized that such proof was impossible, and this led to a revolution in mathematics and then in physics. The two final chapters are devoted to Einstein and his general relativity which revealed to us that the geometry of the world we live in is not Euclidean.Also included is an historical essay on Omar Khayyam, who was not only a poet, but also a brilliant astronomer and mathematician.
Non Euclidean Geometry
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Author : ROBERTO. BONOLA
language : en
Publisher:
Release Date : 2018
Non Euclidean Geometry written by ROBERTO. BONOLA and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Euclidean And Non Euclidean Geometries
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Author : Marvin J. Greenberg
language : en
Publisher:
Release Date : 2020-10-22
Euclidean And Non Euclidean Geometries written by Marvin J. Greenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.
Captain Ahab has an obsessive search for the Great White Whale who had bitten off his leg at the knee.
Leibniz On The Parallel Postulate And The Foundations Of Geometry
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Author : Vincenzo De Risi
language : en
Publisher: Birkhäuser
Release Date : 2016-01-28
Leibniz On The Parallel Postulate And The Foundations Of Geometry written by Vincenzo De Risi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-28 with Mathematics categories.
This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.
Non Euclidean Geometry A Critical And Historical Study Of Its Development Authorized English Translation With Additional Appendices
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Author : Roberto Bonola
language : en
Publisher: Hardpress Publishing
Release Date : 2012-08-01
Non Euclidean Geometry A Critical And Historical Study Of Its Development Authorized English Translation With Additional Appendices written by Roberto Bonola and has been published by Hardpress Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-01 with categories.
Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
The Elements Of Non Euclidean Geometry
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Author : Julian Coolidge
language : en
Publisher:
Release Date : 2013-05-30
The Elements Of Non Euclidean Geometry written by Julian Coolidge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-30 with categories.
The Elements of Non-Euclidean Geometryby Julian Lowell Coolidge Ph.D. - Harvard UniversityContents:CHAPTER IFOUNDATION FOR METRICAL GEOMETRY IN A LIMITED REGIONFundamental assumptions and definitionsSums and differences of distancesSerial arrangement of points on a lineSimple descriptive properties of plane and spaceCHAPTER IICONGRUENT TRANSFORMATIONSAxiom of continuityDivision of distances Measure of distanceAxiom of congruent transformations Definition of angles, their propertiesComparison of trianglesSide of a triangle not greater than sum of other twoComparison and measurement of anglesNature of the congruent groupDefinition of dihedral angles, their propertiesCHAPTER IIITHE THREE HYPOTHESESA variable angle is a continuous function of a variable distanceSaccheri's theorem for isosceles birectangular quadrilateralsThe existence of one rectangle implies the existence of an infinite numberThree assumptions as to the sum of the angles of a right triangleThree assumptions as to the sum of the angles of any triangle, their categorical natureDefinition of the euclidean, hyperbolic, and elliptic hypothesesGeometry in the infinitesimal domain obeys the euclidean hypothesisCHAPTER IVTHE INTRODUCTION OF TRIGONOMETRIC FORMULAELimit of ratio of opposite sides of diminishing isosceles quadrilateralContinuity of the resulting functionIts functional equation and solutionFunctional equation for the cosine of an angleNon-euclidean form for the pythagorean theoremTrigonometric formulae for right and oblique trianglesCHAPTER VANALYTIC FORMULAEDirected distancesGroup of translations of a linePositive and negative directed distancesCoordinates of a point on a lineCoordinates of a point in a planeFinite and infinitesimal distance formulae, the non-euclidean plane as a surface of constant Gaussian curvatureEquation connecting direction cosines of a lineCoordinates of a point in spaceCongruent transformations and orthogonal substitutionsFundamental formulae for distance and angleCHAPTER VICONSISTENCY AND SIGNIFICANCE OF THE AXIOMSExamples of geometries satisfying the assumptions madeRelative independence of the axiomsCHAPTER VIITHE GEOMETRIC AND ANALYTIC EXTENSION OF SPACEPossibility of extending a segment by a definite amount in the euclidean and hyperbolic casesEuclidean and hyperbolic spaceContradiction arising under the elliptic hypothesisNew assumptions identical with the old for limited region, but permitting the extension of every segment by a definite amountLast axiom, free mobility of the whole systemOne to one correspondence of point and coordinate set in euclidean and hyperbolic casesAmbiguity in the elliptic case giving rise to elliptic and spherical geometryIdeal elements, extension of all spaces to be real continuaImaginary elements geometrically defined, extension of all spaces to be perfectcontinua in the complex domainCayleyan Absolute, new form for the definition of distanceExtension of the distance concept to the complex domainCase where a straight line gives a maximum distanceCHAPTER VIIITHE GROUPS OF CONGRUENT TRANSFORMATIONSCongruent transformations of the straight line,, ,, ,, hyperbolic plane,, ,, ,, elliptic plane,, ,, ,, euclidean plane,, ,, ,, hyperbolic space,, ,, ,, elliptic and spherical spaceClifford parallels, or paratactic linesCHAPTER IXPOINT, LINE, AND PLANE TREATED ANALYTICALLYCHAPTER XTHE HIGHER LINE GEOMETRYCHAPTER XITHE CIRCLE AND THE SPHERECHAPTER XIICONIC SECTIONSCHAPTER XIIIQUADRIC SURFACESCHAPTER XIVAREAS AND VOLUMESVolume of a cone of revolution, a sphere, the whole of elliptic or of spherical spaceCHAPTER XVINTRODUCTION TO DIFFERENTIAL GEOMETRYCHAPTER XVIDIFFERENTIAL LINE-GEOMETRYCHAPTER XVIIMULTIPLY CONNECTED SPACESCHAPTER XVIIITHE PROJECTIVE BASIS OF NON-EUCLIDEAN GEOMETRYCHAPTER XIXTHE DIFFERENTIAL BASIS FOR EUCLIDEAN AND NON-EUCLIDEAN GEOMETRY