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Introduction to Non-Euclidean Geometry - Hardcover, by EISENREICH - Good
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Located in: Philadelphia, Pennsylvania, United States
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eBay item number:404943043523
Item specifics
- Condition
- Book Title
- Introduction to Non-Euclidean Geometry
- ISBN
- 9780122748509
- Publication Year
- 1980
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Subject Area
- Mathematics
- Publication Name
- Introduction to Non-Euclidean Geometry
- Publisher
- Elsevier Science & Technology Books
- Subject
- Geometry / Non-Euclidean, Geometry / General
- Number of Pages
- Xii, 274 Pages
About this product
Product Information
An Introduction to Non-Euclidean Geometry covers some introductory topics related to non-Euclidian geometry, including hyperbolic and elliptic geometries. This book is organized into three parts encompassing eight chapters. The first part provides mathematical proofs of Euclid's fifth postulate concerning the extent of a straight line and the theory of parallels. The second part describes some problems in hyperbolic geometry, such as cases of parallels with and without a common perpendicular. This part also deals with horocycles and triangle relations. The third part examines single and double elliptic geometries. This book will be of great value to mathematics, liberal arts, and philosophy major students.
Product Identifiers
Publisher
Elsevier Science & Technology Books
ISBN-10
0122748506
ISBN-13
9780122748509
eBay Product ID (ePID)
1571072
Product Key Features
Publication Name
Introduction to Non-Euclidean Geometry
Format
Hardcover
Language
English
Subject
Geometry / Non-Euclidean, Geometry / General
Publication Year
1980
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xii, 274 Pages
Additional Product Features
LCCN
72-009326
Lc Classification Number
Qa685.G33
Table of Content
Preface Historical Introduction 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 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 Hyperbolic Geometry 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 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 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 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 Elliptic Geometry 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 VIII Single Elliptic Geometry 1. 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
Copyright Date
1973
Target Audience
Scholarly & Professional
Illustrated
Yes
Item description from the seller
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eBay item number:404943043523
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