Non-Euclidean Geometry /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Coxeter, H. S. M.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2014.
Colección:Bibliografija "Spectrum."
Temas:
Geometry, Non-Euclidean.
Géométrie non-euclidienne.
Geometry, Non-Euclidean
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 projectivities2.9 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 transformations4.5 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 DIMENSIONS6.1 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 parallels7.6 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

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