Geometry: a modern introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1973
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Addison-Wesley series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 369 S. Ill. |
Internformat
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| 100 | 1 | |a Keedy, Mervin L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry |b a modern introduction |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1973 | |
| 300 | |a 369 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley series in mathematics | |
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| 700 | 1 | |a Nelson, Charles W. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804135901797810176 |
|---|---|
| adam_text | CONTENTS
Chapter 1 Experimental and Axiomatic Geometry
1. Experimental origin of geometry 1
2. Deductive geometry 2
3. Euclid and axiomatic geometry 3
4. Inductive and deductive reasoning 3
5. Reviewing basic constructions 4
Chapter 2 Points, Lines, and Planes
1. Introduction 14
2. Points 15
3. Geometric figures 16
4. Betweenness 18
5. Assumptions about points and betweenness 21
6. Segments 22
7. Intuition, drawings, and formalism 24
8. Open segments 26
9. Rays and lines 27
10. A point of language 30
11. More about lines and betweenness 32
12. Planes 37
13. Space 39
14. Intersections of lines and planes 41
15. Parallels 42
16. Small abstract deductive systems 44
Chapter 3 Separations, Curves, and Surfaces
1. Introduction 46
2. Separations on a line 46
3. Convex sets 47
4. Separations on a plane 49
5. Curves 58
xi
xii Contents
6. Polygons 60
7. Surfaces 69
Chapter 4 Congruence
1. Introduction 78
2. Congruence of segments 81
3. Congruence for angles 84
4. Congruence for triangles 94
5. More about right angles and perpendiculars 103
6. Bisectors of segments and angles 106
7. Further classification of polygons 109
8. A general concept of congruence Ill
9. Circles and spheres 115
10. Surfaces: an extension 120
11. Maps 123
12. Conic sections 128
Chapter 5 Measures
1. Numeration 133
2. Measures of segments 135
3. Measures of unions of segments 141
4. Some important properties of measures 142
5. Measures of one dimensional figures 145
6. Angle measure 149
7. Some properties of angle measures 151
8. Two dimensional measure or area 152
9. Properties of two dimensional measures 162
10. Three dimensional measure or volume 166
11 Surface area 178
Chapter 6 Parallelism and Similarity
1. Introduction 180
2. Existence of parallels 180
3. The parallel axiom 183
4. More about measures 188
5. Commensurability 190
6. The completeness axiom 193
7. Incommensurability: a problem 198
8. Similarity 200
9. A general concept of similarity 203
10. The ratio of the circumference to the diameter of a circle is constant . 204
11. Applications of similar triangles 207
Chapter 7 Non Euclidean Geometries
1. Euclid s fifth postulate 215
2. Independence of the parallel axiom 218
3. Riemannian geometries 220
4. Bolyai Lobachevskian geometries 223
Contents xiii
5. An infinite but bounded universe 225
6. Euclidean geometry as an approximation 226
Chapter 8 Coordinate Geometry
1. Distance 228
2. Lines 234
3. The general equation of a line 237
4. Half planes 249
5. Subsets of lines 259
6. Applications of analytic methods to geometric proofs 263
Chapter 9 Transformations in a Plane
1. Introduction 269
2. Fundamental motions in a plane 270
3. Combining isometries 278
4. Invariance 283
5. Developing geometry through transformations 287
6. Similarity transformations 291
Chapter 10 Systems of Measures
1. Introduction 300
2. Early units of measure 300
3. Standardization of units of measure 303
4. The British American system of measures 305
5. The metric system 314
6. Relationships between metric and British American units . . . . 316
7. Combinations of units 317
8. Indirect measurement 318
Chapter 11 Errors in Measurement and Calculation with Approximate Data
1. Experimentally determined measures are approximate 321
2. How good is a measurement? 322
3. Calculating with approximate data 326
4. Rounding and significant digits 332
Appendix 335
List of Axioms, Definitions, and Theorems 347
Bibliography 361
Index 363
|
| adam_txt |
CONTENTS
Chapter 1 Experimental and Axiomatic Geometry
1. Experimental origin of geometry 1
2. Deductive geometry 2
3. Euclid and axiomatic geometry 3
4. Inductive and deductive reasoning 3
5. Reviewing basic constructions 4
Chapter 2 Points, Lines, and Planes
1. Introduction 14
2. Points 15
3. Geometric figures 16
4. Betweenness 18
5. Assumptions about points and betweenness 21
6. Segments 22
7. Intuition, drawings, and formalism 24
8. Open segments 26
9. Rays and lines 27
10. A point of language 30
11. More about lines and betweenness 32
12. Planes 37
13. Space 39
14. Intersections of lines and planes 41
15. Parallels 42
16. Small abstract deductive systems 44
Chapter 3 Separations, Curves, and Surfaces
1. Introduction 46
2. Separations on a line 46
3. Convex sets 47
4. Separations on a plane 49
5. Curves 58
xi
xii Contents
6. Polygons 60
7. Surfaces 69
Chapter 4 Congruence
1. Introduction 78
2. Congruence of segments 81
3. Congruence for angles 84
4. Congruence for triangles 94
5. More about right angles and perpendiculars 103
6. Bisectors of segments and angles 106
7. Further classification of polygons 109
8. A general concept of congruence Ill
9. Circles and spheres 115
10. Surfaces: an extension 120
11. Maps 123
12. Conic sections 128
Chapter 5 Measures
1. Numeration 133
2. Measures of segments 135
3. Measures of unions of segments 141
4. Some important properties of measures 142
5. Measures of one dimensional figures 145
6. Angle measure 149
7. Some properties of angle measures 151
8. Two dimensional measure or area 152
9. Properties of two dimensional measures 162
10. Three dimensional measure or volume 166
11 Surface area 178
Chapter 6 Parallelism and Similarity
1. Introduction 180
2. Existence of parallels 180
3. The parallel axiom 183
4. More about measures 188
5. Commensurability 190
6. The completeness axiom 193
7. Incommensurability: a problem 198
8. Similarity 200
9. A general concept of similarity 203
10. The ratio of the circumference to the diameter of a circle is constant . 204
11. Applications of similar triangles 207
Chapter 7 Non Euclidean Geometries
1. Euclid's fifth postulate 215
2. Independence of the parallel axiom 218
3. Riemannian geometries 220
4. Bolyai Lobachevskian geometries 223
Contents xiii
5. An infinite but bounded universe 225
6. Euclidean geometry as an approximation 226
Chapter 8 Coordinate Geometry
1. Distance 228
2. Lines 234
3. The general equation of a line 237
4. Half planes 249
5. Subsets of lines 259
6. Applications of analytic methods to geometric proofs 263
Chapter 9 Transformations in a Plane
1. Introduction 269
2. Fundamental motions in a plane 270
3. Combining isometries 278
4. Invariance 283
5. Developing geometry through transformations 287
6. Similarity transformations 291
Chapter 10 Systems of Measures
1. Introduction 300
2. Early units of measure 300
3. Standardization of units of measure 303
4. The British American system of measures 305
5. The metric system 314
6. Relationships between metric and British American units . . . . 316
7. Combinations of units 317
8. Indirect measurement 318
Chapter 11 Errors in Measurement and Calculation with Approximate Data
1. Experimentally determined measures are approximate 321
2. How good is a measurement? 322
3. Calculating with approximate data 326
4. Rounding and significant digits 332
Appendix 335
List of Axioms, Definitions, and Theorems 347
Bibliography 361
Index 363 |
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| spelling | Keedy, Mervin L. Verfasser aut Geometry a modern introduction 2. ed. Reading, Mass. [u.a.] Addison-Wesley 1973 369 S. Ill. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Geometry Foundations Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s DE-604 Nelson, Charles W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015156322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Geometry a modern introduction |
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