Euclidean geometry and transformations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1972
|
| Schriftenreihe: | Addison-Wesley series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 295 S. Ill. |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
CHAPTER 1 MODERN ELEMENTARY GEOMETRY
1 The Beginnings of Geometry 1
2 Directed segments and angles 4
3 Ideal points and ratios 9
4 The theorem of Menelaus 12
5 Ceva s theorem 19
6 Some geometry of the triangle 25
7 More geometry of the triangle 33
8 Geometric constructions 40
CHAPTER 2 ISOMETRIES IN THE PLANE
9 The Amazing Greeks 48
10 Introduction to translations, rotations, and reflections .... 50
11 Introduction to isometries 55
12 Transformation theory 59
13 Isometries as products of reflections 63
14 Translations and rotations 68
15 Halfturns 72
16 Products of reflections 74
17 Properties of isometries; a summary 77
18 Applications of isometries to elementary geometry 79
19 Further elementary applications 83
20 Advanced applications 87
21 Analytic representations of direct isometries 93
22 Analytic representations of opposite isometries 97
CHAPTER 3 SIMILARITIES IN THE PLANE
23 The rebirth of mathematical thinking 101
24 Introduction to similarities 104
25 Homothety 106
26 Similarity 110
27 Applications of similarities to elementary geometry 114
28 Further elementary applications 119
29 Advanced applications 124
30 Analytic representations of similarities 128
vii
CHAPTER 4 VECTORS AND COMPLEX NUMBERS IN GEOMETRY
31 The search for the meaning of complex numbers 131
32 Introduction to complex numbers 134
33 Vectors 138
34 Vector multiplication 143
35 Vectors and complex numbers 150
36 Triangles in the Gauss plane 155
37 Lines in the Gauss plane 161
38 The circle 165
39 Isometries and similarities in the Gauss plane 168
CHAPTER 5 INVERSION
40 Matchless modern mathematics 171
41 Inversion 175
42 Progressions, ratios, and Peaucellier s cell 180
43 Inversion and complex geometry 185
44 Applications of inversion 189
CHAPTER 6 ISOMETRIES IN SPACE
45 What next? 196
46 Introduction to three dimensions 201
47 Reflection in a plane 204
48 Basic space isometries 208
49 More space isometries 211
50 Some applications 218
51 Analytic representations 222
Appendixes
A. A Summary of Book I of Euclid s Elements 226
B. Basic Ruler and Compass Constructions 228
Bibliography 232
Hints for Selected Exercises 235
Answers 248
Index 288
|
| adam_txt |
CONTENTS
CHAPTER 1 MODERN ELEMENTARY GEOMETRY
1 The Beginnings of Geometry 1
2 Directed segments and angles 4
3 Ideal points and ratios 9
4 The theorem of Menelaus 12
5 Ceva's theorem 19
6 Some geometry of the triangle 25
7 More geometry of the triangle 33
8 Geometric constructions 40
CHAPTER 2 ISOMETRIES IN THE PLANE
9 The Amazing Greeks 48
10 Introduction to translations, rotations, and reflections . 50
11 Introduction to isometries 55
12 Transformation theory 59
13 Isometries as products of reflections 63
14 Translations and rotations 68
15 Halfturns 72
16 Products of reflections 74
17 Properties of isometries; a summary 77
18 Applications of isometries to elementary geometry 79
19 Further elementary applications 83
20 Advanced applications 87
21 Analytic representations of direct isometries 93
22 Analytic representations of opposite isometries 97
CHAPTER 3 SIMILARITIES IN THE PLANE
23 The rebirth of mathematical thinking 101
24 Introduction to similarities 104
25 Homothety 106
26 Similarity 110
27 Applications of similarities to elementary geometry 114
28 Further elementary applications 119
29 Advanced applications 124
30 Analytic representations of similarities 128
vii
CHAPTER 4 VECTORS AND COMPLEX NUMBERS IN GEOMETRY
31 The search for the meaning of complex numbers 131
32 Introduction to complex numbers 134
33 Vectors 138
34 Vector multiplication 143
35 Vectors and complex numbers 150
36 Triangles in the Gauss plane 155
37 Lines in the Gauss plane 161
38 The circle 165
39 Isometries and similarities in the Gauss plane 168
CHAPTER 5 INVERSION
40 Matchless modern mathematics 171
41 Inversion 175
42 Progressions, ratios, and Peaucellier's cell 180
43 Inversion and complex geometry 185
44 Applications of inversion 189
CHAPTER 6 ISOMETRIES IN SPACE
45 What next? 196
46 Introduction to three dimensions 201
47 Reflection in a plane 204
48 Basic space isometries 208
49 More space isometries 211
50 Some applications 218
51 Analytic representations 222
Appendixes
A. A Summary of Book I of Euclid's Elements 226
B. Basic Ruler and Compass Constructions 228
Bibliography 232
Hints for Selected Exercises 235
Answers 248
Index 288 |
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| language | English |
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| spelling | Dodge, Clayton W. Verfasser aut Euclidean geometry and transformations Clayton W. Dodge Reading, Mass. [u.a.] Addison-Wesley 1972 295 S. Ill. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Geometry Transformations (Mathematics) Geometrische Transformation (DE-588)4156725-0 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s DE-604 Geometrische Transformation (DE-588)4156725-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015146763&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dodge, Clayton W. Euclidean geometry and transformations Geometry Transformations (Mathematics) Geometrische Transformation (DE-588)4156725-0 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4156725-0 (DE-588)4020236-7 |
| title | Euclidean geometry and transformations |
| title_auth | Euclidean geometry and transformations |
| title_exact_search | Euclidean geometry and transformations |
| title_exact_search_txtP | Euclidean geometry and transformations |
| title_full | Euclidean geometry and transformations Clayton W. Dodge |
| title_fullStr | Euclidean geometry and transformations Clayton W. Dodge |
| title_full_unstemmed | Euclidean geometry and transformations Clayton W. Dodge |
| title_short | Euclidean geometry and transformations |
| title_sort | euclidean geometry and transformations |
| topic | Geometry Transformations (Mathematics) Geometrische Transformation (DE-588)4156725-0 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometry Transformations (Mathematics) Geometrische Transformation Geometrie |
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