An introduction to non-Euclidean geometry.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Gans, David, 1907-1999
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, Academic Press [1973]
Temas:
Geometry, Non-Euclidean.
G�eom�etrie non-euclidienne.
MATHEMATICS > Geometry > General.
Geometry, Non-Euclidean
Einf�uhrung
Nichteuklidische Geometrie
Niet-Euclidische meetkunde.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • An Introduction to Non-Euclidean Geometry
  • Copyright Page
  • Table of Contents
  • Dedication
  • Preface
  • PART I: HISTORICAL INTRODUCTION
  • Chapter I. Euclid's Fifth Postulate
  • 1. Introduction
  • 2. Euclid's Stated Assumptions
  • 3. The Extent of a Straight Line
  • 4. Euclid's Theory of Parallels
  • 5. Further Consequences of Postulate 5
  • 6. Substitutes for Postulate 5
  • Chapter II. Attempts to Prove the Fifth Postulate
  • 1. Introduction
  • 2. Euclid's Choices
  • 3. Posidonius and His Followers
  • 4. Ptolemy and Proclus
  • 5. Saccheri6. Lambert
  • 7. Legendre
  • 8. The Discovery of Non-Euclidean Geometry
  • PART II: HYPERBOLIC GEOMETRY
  • Chapter III. Parallels With a Common Perpendicular
  • 1. Introduction
  • 2. The Basis E
  • 3. The Initial Theorems of Hyperbolic Geometry
  • 4. The Hyperbolic Parallel Postulate
  • 5. Immediate Consequences of the Postulate
  • 6. Further Properties of Quadrilaterals
  • 7. Parallels With a Common Perpendicular
  • 8. The Angle-Sum of a Triangle
  • 9. The Defect of a Triangle
  • 10. Quadrilaterals Associated with a Triangle
  • 11. The Equivalence of Triangles12. Area of a Triangle
  • 13. Implications of the Area Formula
  • 14. Circles
  • Chapter IV. Parallels Without a Common Perpendicular
  • 1. Introduction
  • 2. Parallels Without a Common Perpendicular
  • 3. Properties of Boundary Parallels
  • 4. Trilateral
  • 5. Angles of Parallelism
  • 6. Distance between Two Lines
  • 7. The Uniqueness of Parallels Without a Common Perpendicular
  • 8. Perpendicular Bisectors of the Sides of a Triangle
  • Chapter V. Horocycles
  • 1. Introduction
  • 2. Corresponding Points
  • 3. Definition of a Horocycle4. Arcs and Chords of a Horocycle
  • 5. Codirectional Horocycles
  • 6. Arc Length on a Horocycle
  • 7. Formulas Related to k-Arcs
  • Chapter VI. Triangle Relations
  • 1. Introduction
  • 2. Associated Right Triangles
  • 3. Improved Angle of Parallelism Formulas
  • 4. Remarks on the Trigonometric Functions
  • 5. Right Triangle Formulas
  • 6. Comparison with Euclidean Formulas
  • 7. Formulas for the General Triangle
  • 8. Hyperbolic Geometry in Small Regions
  • 9. Hyperbolic Geometry and the Physical World
  • PART III: ELLIPTIC GEOMETRYChapter VII. Double Elliptic Geometry
  • 1. Introduction
  • 2. Riemann
  • 3. The Elliptic Geometries
  • 4. Geometry on a Sphere
  • 5. A Description of Double Elliptic Geometry
  • 6. Double Elliptic Geometry and the Physical World
  • 7. An Axiomatic Presentation of Double Elliptic Geometry
  • Chapter VIII. Single Elliptic Geometry
  • 1. Introduction
  • 2. Geometry on a Modified Hemisphere
  • 3. A Description of Single Elliptic Geometry
  • 4. An Axiomatic Presentation of Single Elliptic Geometry

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