Elementary geometry of differentiable curves: an undergraduate introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Pr.
2001
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 216 S. graph. Darst. |
| ISBN: | 0521804531 0521011078 |
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| 245 | 1 | 0 | |a Elementary geometry of differentiable curves |b an undergraduate introduction |c C. G. Gibson |
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Record in the Search Index
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| adam_text | ELEMENTARY GEOMETRY OF DIFFERENTIABLE CURVES: AN UNDERGRADUATE
INTRODUCTION C. G. GIBSON SUB GFITTINGEN 7 213 556 014 2001 A 10468
CAMBRIDGE UNIVERSITY PRESS CONTENTS LIST OF ILLUSTRATIONS PAGE X LIST OF
TABLES XIII PREFACE XIV 1 THE EUCLIDEAN PLANE 1 1.1 THE VECTOR STRUCTURE
1 1.2 THE SCALAR PRODUCT 2 1.3 LENGTH, DISTANCE AND ANGLE 2 1.4 THE
COMPLEX STRUCTURE 6 1.5 LINES 7 1.6 PROJECTION TO LINES 11 2
PARAMETRIZED CURVES 13 2.1 THE GENERAL CONCEPT 13 2.2 SELF CROSSINGS 20
2.3 TANGENT AND NORMAL VECTORS 23 2.4 TANGENT AND NORMAL LINES 27 3
CLASSES OF SPECIAL CURVES 32 3.1 THE STANDARD CONIES 32 3.2 GENERAL
ALGEBRAIC CURVES 38 3.3 TROCHOIDS 42 4 ARC LENGTH 50 4.1 ARC LENGTH 50
4.2 PARAMETRIC EQUIVALENCE 53 4.3 UNIT SPEED CURVES 57 4.4 INVOLUTES 58
5 CURVATURE 62 5.1 THE MOVING FRAME ^ 62 5.2 THE CONCEPT OF CURVATURE 64
5.3 CALCULATING THE CURVATURE 65 VN VIII CONTENTS 5.4 INFLEXIONS 69 5.5
LIMITING BEHAVIOUR 73 6 EXISTENCE AND UNIQUENESS 75 6.1-- ISOMETRIES 76
6.2 FIXED POINTS AND FORMULAS 79 6.3 CONGRUENT CURVES 82 6.4 THE
UNIQUENESS THEOREM 85 7 CONTACT WITH LINES 89 7.1 THE FACTOR THEOREM 89
7.2 MULTIPLICITY OF A ZERO 90 7.3 CONTACT WITH LINES 92 7.4 INFLEXIONS
AND UNDULATIONS 94 7.5 CUSPS 99 8 CONTACT WITH CIRCLES 105 8.1 CONTACT
FUNCTIONS 105 8.2 EVOLUTES 109 8.3 PARALLELS 119 9 VERTICES 124 9.1 THE
CONCEPT OF A VERTEX 124 9.2 APPEARANCE OF VERTICES ON THE EVOLUTE 131
9.3 THE FOUR VERTEX THEOREM 133 10 ENVELOPES 137 10.1 ENVELOPES 137 10.2
THE ENVELOPE THEOREM 140 10.3 NATURAL ENVELOPES IN GEOMETRY 146 11
ORTHOTOMICS 151 11.1 REFLEXIONS 151 11.2 ORTHOTOMICS 153 11.3
ORTHOTOMICS OF NON-REGULAR CURVES 160 11.4 IRREGULAR POINTS ON
ORTHOTOMICS 162 11.5 ANTIORTHOTOMICS 162 12 CAUSTICS BY REFLEXION 165
12.1 CAUSTICS OF A CURVE 166 12.2 CAUSTICS AS EVOLUTES 169 12.3 SOURCES
AT INFINITY 173 12.4 ORTHOTOMICS AS ENVELOPES 177 13 PLANAR KINEMATICS
180 13.1 HISTORICAL GENESIS 180 13.2 PLANAR MOTIONS 184 13.3 GENERAL
ROULETTES 186 CONTENTS IX 14 CENTRODES 190 14.1 GENERIC PARAMETERS 190
14.2 GENERIC PARAMETERS FOR ROULETTES 192 14.3 FIXED AND MOVING
CENTRODES 194 15 GEOMETRY OF TRAJECTORIES 199 15.1 EQUIVALENCE OF
MOTIONS 200 15.2 CUSPS ON TRAJECTORIES 203 15.3 INFLEXIONS ON
TRAJECTORIES 205 15.4 VERTICES ON TRAJECTORIES 209 INDEX 211
|
| any_adam_object | 1 |
| author | Gibson, Christopher G. |
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| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
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| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:50:31Z |
| institution | BVB |
| isbn | 0521804531 0521011078 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009364608 |
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| physical | XVII, 216 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Cambridge Univ. Pr. |
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| spelling | Gibson, Christopher G. Verfasser aut Elementary geometry of differentiable curves an undergraduate introduction C. G. Gibson 1. publ. Cambridge [u.a.] Cambridge Univ. Pr. 2001 XVII, 216 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Courbes Courbes planes Géométrie différentielle ram Curves Kurve (DE-588)4033824-1 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Kurve (DE-588)4033824-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009364608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gibson, Christopher G. Elementary geometry of differentiable curves an undergraduate introduction Courbes Courbes planes Géométrie différentielle ram Curves Kurve (DE-588)4033824-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4033824-1 (DE-588)4012248-7 |
| title | Elementary geometry of differentiable curves an undergraduate introduction |
| title_auth | Elementary geometry of differentiable curves an undergraduate introduction |
| title_exact_search | Elementary geometry of differentiable curves an undergraduate introduction |
| title_full | Elementary geometry of differentiable curves an undergraduate introduction C. G. Gibson |
| title_fullStr | Elementary geometry of differentiable curves an undergraduate introduction C. G. Gibson |
| title_full_unstemmed | Elementary geometry of differentiable curves an undergraduate introduction C. G. Gibson |
| title_short | Elementary geometry of differentiable curves |
| title_sort | elementary geometry of differentiable curves an undergraduate introduction |
| title_sub | an undergraduate introduction |
| topic | Courbes Courbes planes Géométrie différentielle ram Curves Kurve (DE-588)4033824-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Courbes Courbes planes Géométrie différentielle Curves Kurve Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009364608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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