Non-Euclidean geometry /:
The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section 15.9 on the author's useful concept of inversive distance. Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real pr...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Washington, D.C. :
Mathematical Association of America,
[1998]
|
| Ausgabe: | Sixth edition. |
| Schriftenreihe: | MAA spectrum.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section 15.9 on the author's useful concept of inversive distance. Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Transformations that preserve incidence are called colineations. They lead in a natural way to elliptic isometries or "congruent transformations". Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa. This treatment can be enjoyed by anyone who is familiar with algebra up to the elements of group theory. - Publisher |
| Beschreibung: | 1 online resource (xviii, 336 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781614445166 1614445168 |
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| 100 | 1 | |a Coxeter, H. S. M. |q (Harold Scott Macdonald), |d 1907-2003. |1 https://id.oclc.org/worldcat/entity/E39PBJjxtHkqkvw8DwRbYTttKd |0 http://id.loc.gov/authorities/names/n81019969 | |
| 245 | 1 | 0 | |a Non-Euclidean geometry / |c H.S.M. Coxeter. |
| 250 | |a Sixth edition. | ||
| 264 | 1 | |a Washington, D.C. : |b Mathematical Association of America, |c [1998] | |
| 264 | 4 | |c ©1998 | |
| 300 | |a 1 online resource (xviii, 336 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section 15.9 on the author's useful concept of inversive distance. Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Transformations that preserve incidence are called colineations. They lead in a natural way to elliptic isometries or "congruent transformations". Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa. This treatment can be enjoyed by anyone who is familiar with algebra up to the elements of group theory. - Publisher | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a ""Front Cover""; ""NON-EUCLIDEAN GEOMETRY""; ""Copyright Page""; ""PREFACE TO THE SIXTH EDITION""; ""CONTENTS""; ""CHAPTER I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY""; ""1.1 Euclid""; ""1.2 Saccheri and Lambert""; ""1.3 Gauss, Wachter, Schweikart, Taurinus""; ""1.4 Lobatschewsky""; ""1.5 Bolyai""; ""1.6 Riemann""; ""1.7 Klein""; ""CHAPTER II. REAL PROJECTIVE GEOMETRY: FOUNDATIONS""; ""2.1 Definitions and axioms""; ""2.2 Models""; ""2.3 The principle of duality""; ""2.4 Harmonic sets""; ""2.5 Sense""; ""2.6 Triangular and tetrahedral regions""; ""2.7 Ordered correspondences"" | |
| 505 | 8 | |a ""2.8 One-dimensional projectivities""""2.9 Involutions""; ""CHAPTER III. REAL PROJECTIVE GEOMETRY: POLARITIES, CONICS AND QUADRICS""; ""3.1 Two-dimensional projectivities""; ""3.2 Polarities in the plane""; ""3.3 Conies""; ""3.4 Projectivities on a conic""; ""3.5 The fixed points of a collineation""; ""3.6 Cones and reguli""; ""3.7 Three-dimensional projectivities""; ""3.8 Polarities in space""; ""CHAPTER IV. HOMOGENEOUS COORDINATES""; ""4.1 The von Staudt-Hessenberg calculus of points""; ""4.2 One-dimensional projectivities""; ""4.3 Coordinates in one and two dimensions"" | |
| 505 | 8 | |a ""4.4 Collineations and coordinate transformations""""4.5 Polarities""; ""4.6 Coordinates in three dimensions""; ""4.7 Three-dimensional projectivities""; ""4.8 Line coordinates for the generators of a quadric""; ""4.9 Complex projective geometry""; ""CHAPTER V. ELLIPTIC GEOMETRY IN ONE DIMENSION""; ""5.1 Elliptic geometry in general""; ""5.2 Models""; ""5.3 Reflections and translations""; ""5.4 Congruence""; ""5.5 Continuous translation""; ""5.6 The length of a segment""; ""5.7 Distance in terms of cross ratio""; ""5.8 Alternative treatment using the complex line"" | |
| 505 | 8 | |a ""CHAPTER VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS""""6.1 Spherical and elliptic geometry""; ""6.2 Reflection""; ""6.3 Rotations and angles""; ""6.4 Congruence""; ""6.5 Circles""; ""6.6 Composition of rotations""; ""6.7 Formulae for distance and angle""; ""6.8 Rotations and quaternions""; ""6.9 Alternative treatment using the complex plane""; ""CHAPTER VII. ELLIPTIC GEOMETRY IN THREE DIMENSIONS""; ""7.1 Congruent transformations""; ""7.2 Clifford parallels""; ""7.3 The Stephanos-Cartan representation of rotations by points""; ""7.4 Right translations and left translations"" | |
| 505 | 8 | |a ""7.5 Right parallels and left parallels""""7.6 Study's representation of lines by pairs of points""; ""7.7 Clifford translations and quaternions""; ""7.8 Study's coordinates for a line""; ""7.9 Complex space""; ""CHAPTER VIII. DESCRIPTIVE GEOMETRY""; ""8.1 Klein's projective model for hyperbolic geometry""; ""8.2 Geometry in a convex region""; ""8.3 Veblen's axioms of order""; ""8.4 Order in a pencil""; ""8.5 The geometry of lines and planes through a fixed point""; ""8.6 Generalized bundles and pencils""; ""8.7 Ideal points and lines""; ""8.8 Verifying the projective axioms"" | |
| 546 | |a English. | ||
| 650 | 0 | |a Geometry, Non-Euclidean. |0 http://id.loc.gov/authorities/subjects/sh85054155 | |
| 650 | 6 | |a Géométrie non-euclidienne. | |
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| author | Coxeter, H. S. M. (Harold Scott Macdonald), 1907-2003 |
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| author_facet | Coxeter, H. S. M. (Harold Scott Macdonald), 1907-2003 |
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| contents | ""Front Cover""; ""NON-EUCLIDEAN GEOMETRY""; ""Copyright Page""; ""PREFACE TO THE SIXTH EDITION""; ""CONTENTS""; ""CHAPTER I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY""; ""1.1 Euclid""; ""1.2 Saccheri and Lambert""; ""1.3 Gauss, Wachter, Schweikart, Taurinus""; ""1.4 Lobatschewsky""; ""1.5 Bolyai""; ""1.6 Riemann""; ""1.7 Klein""; ""CHAPTER II. REAL PROJECTIVE GEOMETRY: FOUNDATIONS""; ""2.1 Definitions and axioms""; ""2.2 Models""; ""2.3 The principle of duality""; ""2.4 Harmonic sets""; ""2.5 Sense""; ""2.6 Triangular and tetrahedral regions""; ""2.7 Ordered correspondences"" ""2.8 One-dimensional projectivities""""2.9 Involutions""; ""CHAPTER III. REAL PROJECTIVE GEOMETRY: POLARITIES, CONICS AND QUADRICS""; ""3.1 Two-dimensional projectivities""; ""3.2 Polarities in the plane""; ""3.3 Conies""; ""3.4 Projectivities on a conic""; ""3.5 The fixed points of a collineation""; ""3.6 Cones and reguli""; ""3.7 Three-dimensional projectivities""; ""3.8 Polarities in space""; ""CHAPTER IV. HOMOGENEOUS COORDINATES""; ""4.1 The von Staudt-Hessenberg calculus of points""; ""4.2 One-dimensional projectivities""; ""4.3 Coordinates in one and two dimensions"" ""4.4 Collineations and coordinate transformations""""4.5 Polarities""; ""4.6 Coordinates in three dimensions""; ""4.7 Three-dimensional projectivities""; ""4.8 Line coordinates for the generators of a quadric""; ""4.9 Complex projective geometry""; ""CHAPTER V. ELLIPTIC GEOMETRY IN ONE DIMENSION""; ""5.1 Elliptic geometry in general""; ""5.2 Models""; ""5.3 Reflections and translations""; ""5.4 Congruence""; ""5.5 Continuous translation""; ""5.6 The length of a segment""; ""5.7 Distance in terms of cross ratio""; ""5.8 Alternative treatment using the complex line"" ""CHAPTER VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS""""6.1 Spherical and elliptic geometry""; ""6.2 Reflection""; ""6.3 Rotations and angles""; ""6.4 Congruence""; ""6.5 Circles""; ""6.6 Composition of rotations""; ""6.7 Formulae for distance and angle""; ""6.8 Rotations and quaternions""; ""6.9 Alternative treatment using the complex plane""; ""CHAPTER VII. ELLIPTIC GEOMETRY IN THREE DIMENSIONS""; ""7.1 Congruent transformations""; ""7.2 Clifford parallels""; ""7.3 The Stephanos-Cartan representation of rotations by points""; ""7.4 Right translations and left translations"" ""7.5 Right parallels and left parallels""""7.6 Study's representation of lines by pairs of points""; ""7.7 Clifford translations and quaternions""; ""7.8 Study's coordinates for a line""; ""7.9 Complex space""; ""CHAPTER VIII. DESCRIPTIVE GEOMETRY""; ""8.1 Klein's projective model for hyperbolic geometry""; ""8.2 Geometry in a convex region""; ""8.3 Veblen's axioms of order""; ""8.4 Order in a pencil""; ""8.5 The geometry of lines and planes through a fixed point""; ""8.6 Generalized bundles and pencils""; ""8.7 Ideal points and lines""; ""8.8 Verifying the projective axioms"" |
| ctrlnum | (OCoLC)876593007 |
| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Sixth edition. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn876593007 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:54Z |
| institution | BVB |
| isbn | 9781614445166 1614445168 |
| language | English |
| oclc_num | 876593007 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xviii, 336 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Mathematical Association of America, |
| record_format | marc |
| series | MAA spectrum. |
| series2 | Spectrum series |
| spelling | Coxeter, H. S. M. (Harold Scott Macdonald), 1907-2003. https://id.oclc.org/worldcat/entity/E39PBJjxtHkqkvw8DwRbYTttKd http://id.loc.gov/authorities/names/n81019969 Non-Euclidean geometry / H.S.M. Coxeter. Sixth edition. Washington, D.C. : Mathematical Association of America, [1998] ©1998 1 online resource (xviii, 336 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Spectrum series Includes bibliographical references and index. The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section 15.9 on the author's useful concept of inversive distance. Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Transformations that preserve incidence are called colineations. They lead in a natural way to elliptic isometries or "congruent transformations". Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa. This treatment can be enjoyed by anyone who is familiar with algebra up to the elements of group theory. - Publisher Print version record. ""Front Cover""; ""NON-EUCLIDEAN GEOMETRY""; ""Copyright Page""; ""PREFACE TO THE SIXTH EDITION""; ""CONTENTS""; ""CHAPTER I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY""; ""1.1 Euclid""; ""1.2 Saccheri and Lambert""; ""1.3 Gauss, Wachter, Schweikart, Taurinus""; ""1.4 Lobatschewsky""; ""1.5 Bolyai""; ""1.6 Riemann""; ""1.7 Klein""; ""CHAPTER II. REAL PROJECTIVE GEOMETRY: FOUNDATIONS""; ""2.1 Definitions and axioms""; ""2.2 Models""; ""2.3 The principle of duality""; ""2.4 Harmonic sets""; ""2.5 Sense""; ""2.6 Triangular and tetrahedral regions""; ""2.7 Ordered correspondences"" ""2.8 One-dimensional projectivities""""2.9 Involutions""; ""CHAPTER III. REAL PROJECTIVE GEOMETRY: POLARITIES, CONICS AND QUADRICS""; ""3.1 Two-dimensional projectivities""; ""3.2 Polarities in the plane""; ""3.3 Conies""; ""3.4 Projectivities on a conic""; ""3.5 The fixed points of a collineation""; ""3.6 Cones and reguli""; ""3.7 Three-dimensional projectivities""; ""3.8 Polarities in space""; ""CHAPTER IV. HOMOGENEOUS COORDINATES""; ""4.1 The von Staudt-Hessenberg calculus of points""; ""4.2 One-dimensional projectivities""; ""4.3 Coordinates in one and two dimensions"" ""4.4 Collineations and coordinate transformations""""4.5 Polarities""; ""4.6 Coordinates in three dimensions""; ""4.7 Three-dimensional projectivities""; ""4.8 Line coordinates for the generators of a quadric""; ""4.9 Complex projective geometry""; ""CHAPTER V. ELLIPTIC GEOMETRY IN ONE DIMENSION""; ""5.1 Elliptic geometry in general""; ""5.2 Models""; ""5.3 Reflections and translations""; ""5.4 Congruence""; ""5.5 Continuous translation""; ""5.6 The length of a segment""; ""5.7 Distance in terms of cross ratio""; ""5.8 Alternative treatment using the complex line"" ""CHAPTER VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS""""6.1 Spherical and elliptic geometry""; ""6.2 Reflection""; ""6.3 Rotations and angles""; ""6.4 Congruence""; ""6.5 Circles""; ""6.6 Composition of rotations""; ""6.7 Formulae for distance and angle""; ""6.8 Rotations and quaternions""; ""6.9 Alternative treatment using the complex plane""; ""CHAPTER VII. ELLIPTIC GEOMETRY IN THREE DIMENSIONS""; ""7.1 Congruent transformations""; ""7.2 Clifford parallels""; ""7.3 The Stephanos-Cartan representation of rotations by points""; ""7.4 Right translations and left translations"" ""7.5 Right parallels and left parallels""""7.6 Study's representation of lines by pairs of points""; ""7.7 Clifford translations and quaternions""; ""7.8 Study's coordinates for a line""; ""7.9 Complex space""; ""CHAPTER VIII. DESCRIPTIVE GEOMETRY""; ""8.1 Klein's projective model for hyperbolic geometry""; ""8.2 Geometry in a convex region""; ""8.3 Veblen's axioms of order""; ""8.4 Order in a pencil""; ""8.5 The geometry of lines and planes through a fixed point""; ""8.6 Generalized bundles and pencils""; ""8.7 Ideal points and lines""; ""8.8 Verifying the projective axioms"" English. Geometry, Non-Euclidean. http://id.loc.gov/authorities/subjects/sh85054155 Géométrie non-euclidienne. MATHEMATICS Geometry General. bisacsh MATHEMATICS Geometry Non-Euclidean. bisacsh Geometry, Non-Euclidean fast has work: Non-Euclidean geometry (Text) https://id.oclc.org/worldcat/entity/E39PCH6XYGGdXKDGWt3wKBJYyd https://id.oclc.org/worldcat/ontology/hasWork Print version: Coxeter, H.S.M. (Harold Scott Macdonald), 1907-2003. Non-Euclidean geometry. Sixth edition 0883855224 (DLC) 98085640 (OCoLC)40074192 MAA spectrum. http://id.loc.gov/authorities/names/n91122167 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=759515 Volltext |
| spellingShingle | Coxeter, H. S. M. (Harold Scott Macdonald), 1907-2003 Non-Euclidean geometry / MAA spectrum. ""Front Cover""; ""NON-EUCLIDEAN GEOMETRY""; ""Copyright Page""; ""PREFACE TO THE SIXTH EDITION""; ""CONTENTS""; ""CHAPTER I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY""; ""1.1 Euclid""; ""1.2 Saccheri and Lambert""; ""1.3 Gauss, Wachter, Schweikart, Taurinus""; ""1.4 Lobatschewsky""; ""1.5 Bolyai""; ""1.6 Riemann""; ""1.7 Klein""; ""CHAPTER II. REAL PROJECTIVE GEOMETRY: FOUNDATIONS""; ""2.1 Definitions and axioms""; ""2.2 Models""; ""2.3 The principle of duality""; ""2.4 Harmonic sets""; ""2.5 Sense""; ""2.6 Triangular and tetrahedral regions""; ""2.7 Ordered correspondences"" ""2.8 One-dimensional projectivities""""2.9 Involutions""; ""CHAPTER III. REAL PROJECTIVE GEOMETRY: POLARITIES, CONICS AND QUADRICS""; ""3.1 Two-dimensional projectivities""; ""3.2 Polarities in the plane""; ""3.3 Conies""; ""3.4 Projectivities on a conic""; ""3.5 The fixed points of a collineation""; ""3.6 Cones and reguli""; ""3.7 Three-dimensional projectivities""; ""3.8 Polarities in space""; ""CHAPTER IV. HOMOGENEOUS COORDINATES""; ""4.1 The von Staudt-Hessenberg calculus of points""; ""4.2 One-dimensional projectivities""; ""4.3 Coordinates in one and two dimensions"" ""4.4 Collineations and coordinate transformations""""4.5 Polarities""; ""4.6 Coordinates in three dimensions""; ""4.7 Three-dimensional projectivities""; ""4.8 Line coordinates for the generators of a quadric""; ""4.9 Complex projective geometry""; ""CHAPTER V. ELLIPTIC GEOMETRY IN ONE DIMENSION""; ""5.1 Elliptic geometry in general""; ""5.2 Models""; ""5.3 Reflections and translations""; ""5.4 Congruence""; ""5.5 Continuous translation""; ""5.6 The length of a segment""; ""5.7 Distance in terms of cross ratio""; ""5.8 Alternative treatment using the complex line"" ""CHAPTER VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS""""6.1 Spherical and elliptic geometry""; ""6.2 Reflection""; ""6.3 Rotations and angles""; ""6.4 Congruence""; ""6.5 Circles""; ""6.6 Composition of rotations""; ""6.7 Formulae for distance and angle""; ""6.8 Rotations and quaternions""; ""6.9 Alternative treatment using the complex plane""; ""CHAPTER VII. ELLIPTIC GEOMETRY IN THREE DIMENSIONS""; ""7.1 Congruent transformations""; ""7.2 Clifford parallels""; ""7.3 The Stephanos-Cartan representation of rotations by points""; ""7.4 Right translations and left translations"" ""7.5 Right parallels and left parallels""""7.6 Study's representation of lines by pairs of points""; ""7.7 Clifford translations and quaternions""; ""7.8 Study's coordinates for a line""; ""7.9 Complex space""; ""CHAPTER VIII. DESCRIPTIVE GEOMETRY""; ""8.1 Klein's projective model for hyperbolic geometry""; ""8.2 Geometry in a convex region""; ""8.3 Veblen's axioms of order""; ""8.4 Order in a pencil""; ""8.5 The geometry of lines and planes through a fixed point""; ""8.6 Generalized bundles and pencils""; ""8.7 Ideal points and lines""; ""8.8 Verifying the projective axioms"" Geometry, Non-Euclidean. http://id.loc.gov/authorities/subjects/sh85054155 Géométrie non-euclidienne. MATHEMATICS Geometry General. bisacsh MATHEMATICS Geometry Non-Euclidean. bisacsh Geometry, Non-Euclidean fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85054155 |
| title | Non-Euclidean geometry / |
| title_auth | Non-Euclidean geometry / |
| title_exact_search | Non-Euclidean geometry / |
| title_full | Non-Euclidean geometry / H.S.M. Coxeter. |
| title_fullStr | Non-Euclidean geometry / H.S.M. Coxeter. |
| title_full_unstemmed | Non-Euclidean geometry / H.S.M. Coxeter. |
| title_short | Non-Euclidean geometry / |
| title_sort | non euclidean geometry |
| topic | Geometry, Non-Euclidean. http://id.loc.gov/authorities/subjects/sh85054155 Géométrie non-euclidienne. MATHEMATICS Geometry General. bisacsh MATHEMATICS Geometry Non-Euclidean. bisacsh Geometry, Non-Euclidean fast |
| topic_facet | Geometry, Non-Euclidean. Géométrie non-euclidienne. MATHEMATICS Geometry General. MATHEMATICS Geometry Non-Euclidean. Geometry, Non-Euclidean |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=759515 |
| work_keys_str_mv | AT coxeterhsm noneuclideangeometry |