Verfügbarkeit: Elementary geometry of differentiable curves

Elementary geometry of differentiable curves: an undergraduate introduction

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Bibliographische Detailangaben
Beteilige Person:	Gibson, Christopher G. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Pr. 2001
Ausgabe:	1. publ.
Schlagwörter:	Courbes Courbes planes Géométrie différentielle Curves Kurve Differentialgeometrie
Links:	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
Umfang:	XVII, 216 S. graph. Darst.
ISBN:	0521804531 0521011078

Internformat

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Datensatz im Suchindex

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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
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indexdate	2024-12-20T10:52:06Z
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isbn	0521804531 0521011078
language	English
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owner	DE-824 DE-384 DE-1050 DE-703 DE-634 DE-11
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publisher	Cambridge Univ. Pr.
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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
work_keys_str_mv	AT gibsonchristopherg elementarygeometryofdifferentiablecurvesanundergraduateintroduction

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