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Introduction to Non-Euclidean Geometry.

Author: EISENREICH.
Publisher: Elsevier Science, 2014.
Edition/Format:   eBook : Document : English
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Genre/Form: Electronic books
Additional Physical Format: Erscheint auch als:
EISENREICH. Introduction to Non-Euclidean Geometry
Druck-Ausgabe
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: EISENREICH.
ISBN: 1322478791 9781322478791 9781483295312 1483295311
OCLC Number: 898326880
Description: 1 online resource
Contents: 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. Saccheri; 6. Lambert; 7. Legendre; 8. The Discovery of Non-Euclidean Geometry. PART II: HYPERBOLIC GEOMETRYChapter 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 Triangles; 12. Area of a Triangle; 13. Implications of the Area Formula; 14. Circles; Chapter IV. Parallels Without a Common Perpendicular. 1. Introduction2. 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 Horocycle; 4. 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 Formulas4. 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 GEOMETRY; Chapter 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 Geometry1. Intoduction; 2. Geometry on a Modified Hemisphere; 3. A Description of Single Elliptic Geometry; 4. An Axiomatic Presentation of Single Elliptic Geometry; Appendix: A Summary from Euclid's Elements; Bibliography; Answers to Selected Exercises; Index.

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