Introduction to geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1989
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley classics library
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XVI, 469 S. Ill., graph. Darst. |
| ISBN: | 0471504580 |
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Datensatz im Suchindex
| _version_ | 1804138956443353088 |
|---|---|
| adam_text | INTRODUCTION TO GEOMETRY SECOND EDITION H. S. M. COXETER, F. R. S.
PROFESSOR OF MATHEMATICS UNIVERSITY OF TORONTO WILEY CLASSICS LIBRARY
EDITION PUBLISHED 1989 WILEY JOHN WILEY & SONS, INC. CONTENTS PART I
TRIANGLES 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 EUCLID PRIMITIVE CONCEPTS
AND AXIOMS PORTS ASINORUM THE MEDIANS AND THE CENTROID THE INCIRCLE AND
THE CIRCUMCIRCLE THE EULER LINE AND THE ORTHOCENTER THE NINE-POINT
CIRCLE TWO EXTREMUM PROBLEMS MORLEY S THEOREM 3 4 6 10 11 17 18 20 23 2
REGULAR POLYGONS 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 CYCLOTOMY ANGLE
TRISECTION ISOMETRY SYMMETRY GROUPS THE PRODUCT OF TWO REFLECTIONS THE
KALEIDOSCOPE STAR POLYGONS 26 26 28 29 30 31 33 34 36 3 ISOMETRY IN THE
EUCLIDEAN PLANE 3.1 DIRECT AND OPPOSITE ISOMETRIES 3.2 TRANSLATION 3.3
GLIDE REFLECTION 3.4 REFLECTIONS AND HALF-TURNS 3.5 SUMMARY OF RESULTS
ON ISOMETRIES 39 39 41 43 45 45 XI XLL CONTENTS 3.6 HJELMSLEV S THEOREM
46 3.7 PATTERNS ON A STRIP 47 4 TWO-DIMENSIONAL CRYSTALLOGRAPHY 50 4.1
LATTICES AND THEIR DIRICHLET REGIONS 50 4.2 THE SYMMETRY GROUP OF THE
GENERAL LATTICE 54 4.3 THE ART OF M. C. ESCHER 57 4.4 SIX PATTERNS OF
BRICKS 58 4.5 THE CRYSTALLOGRAPHIC RESTRICTION 60 4.6 REGULAR
TESSELLATIONS 61 4.7 SYLVESTER S PROBLEM OF COLLINEAR POINTS 65 5
SIMILARITY IN THE EUCLIDEAN PLANE 67 5.1 DILATATION 67 5.2 CENTERS OF
SIMILITUDE 70 5.3 THE NINE-POINT CENTER 71 5.4 THE INVARIANT POINT OF A
SIMILARITY 72 5.5 DIRECT SIMILARITY 73 5.6 OPPOSITE SIMILARITY 74 6
CIRCLES AND SPHERES 77 6.1 INVERSION IN A CIRCLE 77 6.2 ORTHOGONAL
CIRCLES 79 6.3 INVERSION OF LINES AND CIRCLES 80 6.4 THE INVERSIVE PLANE
83 6.5 COAXAL CIRCLES 85 6.6 THE CIRCLE OF APOLLONIUS 88 6.7
CIRCLE-PRESERVING TRANSFORMATIONS 90 6.8 INVERSION IN A SPHERE 91 6.9
THE ELLIPTIC PLANE 92 7 ISOMETRY AND SIMILARITY IN EUCLIDEAN SPACE 96
7.1 DIRECT AND OPPOSITE ISOMETRIES 96 7.2 THE CENTRAL INVERSION 98 7.3
ROTATION AND TRANSLATION 98 7.4 THE PRODUCT OF THREE REFLECTIONS 99 7.5
TWIST 100 7.6 DILATIVE ROTATION 101 7.7 SPHERE-PRESERVING
TRANSFORMATIONS 104 CONTENTS XIII PART II COORDINATES 8.1 8.2 8.3 8.4
8.5 8.6 8.7 8.8 CARTESIAN COORDINATES POLAR COORDINATES THE CIRCLE
CONIES TANGENT, ARC LENGTH, AND AREA HYPERBOLIC FUNCTIONS THE
EQUIANGULAR SPIRAL THREE DIMENSIONS 107 107 110 113 115 119 124 125 127
9 COMPLEX NUMBERS 9.1 RATIONAL NUMBERS 9.2 REAL NUMBERS 9.3 THE ARGAND
DIAGRAM 9.4 MODULUS AND AMPLITUDE 9.5 THE FORMULA E VI + 1 = 0 9.6 ROOTS
OF EQUATIONS 9.7 CONFORMAL TRANSFORMATIONS 135 135 137 138 141 143 144
145 THE FIVE PLATONIC SOLIDS 10.1 PYRAMIDS, PRISMS, AND ANTIPRISMS 10.2
DRAWINGS AND MODELS 10.3 EULER S FORMULA 10.4 RADII AND ANGLES 10.5
RECIPROCAL POLYHEDRA 148 148 150 152 155 157 THE GOLDEN SECTION AND
PHYLLOTAXIS 11.1 EXTREME AND MEAN RATIO 11.2 DE DIVINA PROPORTIONE 11.3
THE GOLDEN SPIRAL 11.4 THE FIBONACCI NUMBERS 11.5 PHYLLOTAXIS 160 160
162 164 165 169 XLV CONTENTS PART III 12 ORDERED GEOMETRY 175 12.1 THE
EXTRACTION OF TWO DISTINCT GEOMETRIES FROM EUCLID 175 12.2 INTERMEDIACY
177 12.3 SYLVESTER S PROBLEM OF COLLINEAR POINTS 181 12.4 PLANES AND
HYPERPLANES 183 12.5 CONTINUITY 186 12.6 PARALLELISM 187 13 AFFINE
GEOMETRY 191 13.1 THE AXIOM OF PARALLELISM AND THE DESARGUES AXIOM 191
13.2 DILATATIONS 193 13.3 AFFINITIES 199 13.4 EQUIAFFINITIES 203 13.5
TWO-DIMENSIONAL LATTICES 208 13.6 VECTORS AND CENTROIDS 212 13.7
BARYCENTRIC COORDINATES 216 13.8 AFFINE SPACE 222 13.9 THREE-DIMENSIONAL
LATTICES 225 14 PROJECTIVE GEOMETRY 229 14.1 AXIOMS FOR THE GENERAL
PROJECTIVE PLANE 230 14.2 PROJECTIVE COORDINATES 234 14.3 DESARGUES S
THEOREM 238 14.4 QUADRANGULAR AND HARMONIC SETS 239 14.5 PROJECTIVITIES
242 14.6 COLLINEATIONS AND CORRELATIONS 247 14.7 THE CONIC 252 14.8
PROJECTIVE SPACE 256 14.9 EUCLIDEAN SPACE 261 15 ABSOLUTE GEOMETRY 263
15.1 CONGRUENCE 263 15.2 PARALLELISM 265 15.3 ISOMETRY 268 15.4 FINITE
GROUPS OF ROTATIONS 270 15.5 FINITE GROUPS OF ISOMETRIES 277 15.6
GEOMETRICAL CRYSTALLOGRAPHY 278 CONTENTS 15.7 THE POLYHEDRAL
KALEIDOSCOPE 15.8 DISCRETE GROUPS GENERATED BY INVERSIONS 279 282 16
HYPERBOLIC GEOMETRY 287 16.1 THE EUCLIDEAN AND HYPERBOLIC AXIOMS OF
PARALLELISM 287 16.2 THE QUESTION OF CONSISTENCY 288 16.3 THE ANGLE OF
PARALLELISM 291 16.4 THE FINITENESS OF TRIANGLES 295 16.5 AREA AND
ANGULAR DEFECT 296 16.6 CIRCLES, HOROCYCLES, AND EQUIDISTANT CURVES 300
16.7 POINCARE S HALF-PLANE MODEL 302 16.8 THE HOROSPHERE AND THE
EUCLIDEAN PLANE 303 PARTIV 17 DIFFERENTIAL GEOMETRY OF CURVES 17.1
VECTORS IN EUCLIDEAN SPACE 17.2 VECTOR FUNCTIONS AND THEIR DERIVATIVES
17.3 CURVATURE, EVOLUTES, AND INVOLUTES 17.4 THE CATENARY 17.5 THE
TRACTRIX 17.6 TWISTED CURVES 17.7 THE CIRCULAR HELIX 17.8 THE GENERAL
HELIX 17.9 THE CONCHO-SPIRAL 307 307 312 313 317 319 321 323 325 326 18
THE TENSOR NOTATION 18.1 DUAL BASES 18.2 THE FUNDAMENTAL TENSOR 18.3
RECIPROCAL LATTICES 18.4 THE CRITICAL LATTICE OF A SPHERE 18.5 GENERAL
COORDINATES 18.6 THE ALTERNATING SYMBOL 328 328 329 332 335 337 341 19
DIFFERENTIAL GEOMETRY OF SURFACES 19.1 THE USE OF TWO PARAMETERS ON A
SURFACE 19.2 DIRECTIONS ON A SURFACE 19.3 NORMAL CURVATURE 342 342 345
349 XVL CONTENTS 19.4 PRINCIPAL CURVATURES 352 19.5 PRINCIPAL DIRECTIONS
AND LINES OF CURVATURE 356 19.6 UMBILICS 359 19.7 DUPIN S THEOREM AND
LIOUVILLE S THEOREM 361 19.8 DUPIN S INDICATRIX 363 20 GEODESICS 366
20.1 THEOREMA EGREGIUM 366 20.2 THE DIFFERENTIAL EQUATIONS FOR GEODESIES
369 20.3 THE INTEGRAL CURVATURE OF A GEODESIC TRIANGLE 372 20.4 THE
EULER-POINCAR6 CHARACTERISTIC 373 20.5 SURFACES OF CONSTANT CURVATURE
375 20.6 THE ANGLE OF PARALLELISM 376 20.7 THE PSEUDOSPHERE 377 21
TOPOLOGY OF SURFACES 379 21.1 ORIENTABLE SURFACES 380 21.2 NONORIENTABLE
SURFACES 382 21.3 REGULAR MAPS 385 21.4 THE FOUR-COLOR PROBLEM 389 21.5
THE SIX-COLOR THEOREM 391 21.6 A SUFFICIENT NUMBER OF COLORS FOR ANY
SURFACE 393 21.7 SURFACES THAT NEED THE FULL NUMBER OF COLORS 394 22
FOUR-DIMENSIONAL GEOMETRY 396 22.1 THE SIMPLEST FOUR-DIMENSIONAL FIGURES
397 22.2 A NECESSARY CONDITION FOR THE EXISTENCE OF { P, Q, R) 399 22.3
CONSTRUCTIONS FOR REGULAR POLYTOPES 401 22.4 CLOSE PACKING OF EQUAL
SPHERES 405 22.5 A STATISTICAL HONEYCOMB 411 TABLES 413 REFERENCES 415
ANSWERS TO EXERCISES 419 459 INDEX
|
| any_adam_object | 1 |
| author | Coxeter, Harold S. M. 1907-2003 |
| author_GND | (DE-588)118522507 |
| author_facet | Coxeter, Harold S. M. 1907-2003 |
| author_role | aut |
| author_sort | Coxeter, Harold S. M. 1907-2003 |
| author_variant | h s m c hsm hsmc |
| building | Verbundindex |
| bvnumber | BV023769436 |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)844938398 (DE-599)BVBBV023769436 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 0471504580 |
| language | English |
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| spelling | Coxeter, Harold S. M. 1907-2003 Verfasser (DE-588)118522507 aut Introduction to geometry H. S. M. Coxeter 2. ed. New York [u.a.] Wiley 1989 XVI, 469 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley classics library Hier auch später erschienene, unveränderte Nachdrucke Geometrie (DE-588)4020236-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Geometrie (DE-588)4020236-7 s DE-604 Differentialgeometrie (DE-588)4012248-7 s 2\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017411673&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Coxeter, Harold S. M. 1907-2003 Introduction to geometry Geometrie (DE-588)4020236-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4012248-7 (DE-588)4151278-9 |
| title | Introduction to geometry |
| title_auth | Introduction to geometry |
| title_exact_search | Introduction to geometry |
| title_full | Introduction to geometry H. S. M. Coxeter |
| title_fullStr | Introduction to geometry H. S. M. Coxeter |
| title_full_unstemmed | Introduction to geometry H. S. M. Coxeter |
| title_short | Introduction to geometry |
| title_sort | introduction to geometry |
| topic | Geometrie (DE-588)4020236-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometrie Differentialgeometrie Einführung |
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