Yearning for the impossible: the surprising truths of mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wellesley, Mass.
Peters
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 230 S. Ill., graph. Darst. |
| ISBN: | 156881254X 9781568812540 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | YEARNING FOR THE IMPOSSIBLE THE SURPRISING TRUTHS OF MATHEMATICS JOHN
STILLWELL UNIVERSITY OF SAN FRANCISCO A K PETERS, LTD. WELLESLEY,
MASSACHUSETTS CONTENTS PREFACE , XI 1 THE IRRATIONAL 1 1.1 THE
PYTHAGOREAN DREAM 2 1.2 THE PYTHAGOREAN THEOREM 5 1.3 IRRATIONAL
TRIANGLES 7 1.4 THE PYTHAGOREAN NIGHTMARE 10 1.5 EXPLAINING THE
IRRATIONAL 12 1.6 THE CONTINUED FRACTION FOR S/L 16 1.7 EQUAL
TEMPERAMENT 20 2 THE IMAGINARY 25 2.1 NEGATIVE NUMBERS 26 2.2 IMAGINARY
NUMBERS 29 2.3 SOLVING CUBIC EQUATIONS 30 2.4 REAL SOLUTIONS VIA
IMAGINARY NUMBERS 32 2.5 WHERE WERE IMAGINARY NUMBERS BEFORE 1572? 33
2.6 GEOMETRY OF MULTIPLICATION 36 2.7 COMPLEX NUMBERS GIVE MORE THAN WE
ASKED FOR 40 2.8 WHY CALL THEM COMPLEX NUMBERS? 44 3 THE HORIZON 47
3.1 PARALLEL LINES 49 3.2 COORDINATES 51 3.3 PARALLEL LINES AND VISION
54 3.4 DRAWING WITHOUT MEASUREMENT 59 3.5 THE THEOREMS OF PAPPUS AND
DESARGUES 62 3.6 THE LITTLE DESARGUES THEOREM 66 VU VIII CONTENTS 3.7
WHAT ARE THE LAWS OF ALGEBRA? 69 3.8 PROJECTIVE ADDITION AND
MULTIPLICATION 72 4 THE INFINITESIMAL 77 4.1 LENGTH AND AREA 78 4.2
VOLUME 79 4.3 VOLUME OF A TETRAHEDRON 81 4.4 THE CIRCLE 84 4.5 THE
PARABOLA 87 4.6 THE SLOPES OF OTHER CURVES 90 4.7 SLOPE AND AREA 93 4.8
THE VALUE OF N 96 4.9 GHOSTS OF DEPARTED QUANTITIES 98 5 CURVED SPACE
101 5.1 FLAT SPACE AND MEDIEVAL SPACE 102 5.2 THE 2-SPHERE AND THE
3-SPHERE 104 5.3 FLAT SURFACES AND THE PARALLEL AXIOM 108 5.4 THE SPHERE
AND THE PARALLEL AXIOM ILL 5.5 NON-EUCLIDEAN GEOMETRY 114 5.6 NEGATIVE
CURVATURE 116 5.7 THE HYPERBOLIC PLANE 119 5.8 HYPERBOLIC SPACE 123 5.9
MATHEMATICAL SPACE AND ACTUAL SPACE 124 6 THE FOURTH DIMENSION 129 6.1
ARITHMETIC OF PAIRS 130 6.2 SEARCHING FOR AN ARITHMETIC OF TRIPLES 131
6.3 WHY RC-TUPLES ARE UNLIKE NUMBERS WHEN N 3 132 6.4 QUATERNIONS 135
6.5 THE FOUR-SQUARE THEOREM 139 6.6 QUATERNIONS AND SPACE ROTATIONS 141
6.7 SYMMETRY IN THREE DIMENSIONS 144 6.8 TETRAHEDRAL SYMMETRY AND THE
24-CELL 146 6.9 THE REGULAR POLYTOPES 150 7 THE IDEAL 155 7.1 DISCOVERY
AND INVENTION 156 7.2 DIVISION WITH REMAINDER 158 7.3 UNIQUE PRIME
FACTORIZATION 161 CONTENTS IX 7.4 GAUSSIAN INTEGERS 163 7.5 GAUSSIAN
PRIMES 166 7.6 RATIONAL SLOPES AND RATIONAL ANGLES 168 7.7 UNIQUE PRIME
FACTORIZATION LOST 169 7.8 IDEALS, OR UNIQUE PRIME FACTORIZATION
REGAINED 172 8 PERIODIC SPACE 177 8.1 THE IMPOSSIBLE TRIBAR 178 8.2 THE
CYLINDER AND THE PLANE 180 8.3 WHERE THE WILD THINGS ARE 183 8.4
PERIODIC WORLDS 185 8.5 PERIODICITY AND TOPOLOGY 187 8.6 A BRIEF HISTORY
OF PERIODICITY 190 9 THE INFINITE 197 9.1 FINITE AND INFINITE 198 9.2
POTENTIAL AND ACTUAL INFINITY 199 9.3 THE UNCOUNTABLE 201 9.4 THE
DIAGONAL ARGUMENT 203 9.5 THE TRANSCENDENTAL 205 9.6 YEARNING FOR
COMPLETENESS 208 EPILOGUE 211 INDEX L4R TEUE^JU $.
|
| adam_txt |
YEARNING FOR THE IMPOSSIBLE THE SURPRISING TRUTHS OF MATHEMATICS JOHN
STILLWELL UNIVERSITY OF SAN FRANCISCO A K PETERS, LTD. WELLESLEY,
MASSACHUSETTS CONTENTS PREFACE , XI 1 THE IRRATIONAL 1 1.1 THE
PYTHAGOREAN DREAM 2 1.2 THE PYTHAGOREAN THEOREM 5 1.3 IRRATIONAL
TRIANGLES 7 1.4 THE PYTHAGOREAN NIGHTMARE 10 1.5 EXPLAINING THE
IRRATIONAL 12 1.6 THE CONTINUED FRACTION FOR S/L 16 1.7 EQUAL
TEMPERAMENT 20 2 THE IMAGINARY 25 2.1 NEGATIVE NUMBERS 26 2.2 IMAGINARY
NUMBERS 29 2.3 SOLVING CUBIC EQUATIONS 30 2.4 REAL SOLUTIONS VIA
IMAGINARY NUMBERS 32 2.5 WHERE WERE IMAGINARY NUMBERS BEFORE 1572? 33
2.6 GEOMETRY OF MULTIPLICATION 36 2.7 COMPLEX NUMBERS GIVE MORE THAN WE
ASKED FOR 40 2.8 WHY CALL THEM "COMPLEX" NUMBERS? 44 3 THE HORIZON 47
3.1 PARALLEL LINES 49 3.2 COORDINATES 51 3.3 PARALLEL LINES AND VISION
54 3.4 DRAWING WITHOUT MEASUREMENT 59 3.5 THE THEOREMS OF PAPPUS AND
DESARGUES 62 3.6 THE LITTLE DESARGUES THEOREM 66 VU VIII CONTENTS 3.7
WHAT ARE THE LAWS OF ALGEBRA? 69 3.8 PROJECTIVE ADDITION AND
MULTIPLICATION 72 4 THE INFINITESIMAL 77 4.1 LENGTH AND AREA 78 4.2
VOLUME 79 4.3 VOLUME OF A TETRAHEDRON 81 4.4 THE CIRCLE 84 4.5 THE
PARABOLA 87 4.6 THE SLOPES OF OTHER CURVES 90 4.7 SLOPE AND AREA 93 4.8
THE VALUE OF N 96 4.9 GHOSTS OF DEPARTED QUANTITIES 98 5 CURVED SPACE
101 5.1 FLAT SPACE AND MEDIEVAL SPACE 102 5.2 THE 2-SPHERE AND THE
3-SPHERE 104 5.3 FLAT SURFACES AND THE PARALLEL AXIOM 108 5.4 THE SPHERE
AND THE PARALLEL AXIOM ILL 5.5 NON-EUCLIDEAN GEOMETRY 114 5.6 NEGATIVE
CURVATURE 116 5.7 THE HYPERBOLIC PLANE 119 5.8 HYPERBOLIC SPACE 123 5.9
MATHEMATICAL SPACE AND ACTUAL SPACE 124 6 THE FOURTH DIMENSION 129 6.1
ARITHMETIC OF PAIRS 130 6.2 SEARCHING FOR AN ARITHMETIC OF TRIPLES 131
6.3 WHY RC-TUPLES ARE UNLIKE NUMBERS WHEN N 3 132 6.4 QUATERNIONS 135
6.5 THE FOUR-SQUARE THEOREM 139 6.6 QUATERNIONS AND SPACE ROTATIONS 141
6.7 SYMMETRY IN THREE DIMENSIONS 144 6.8 TETRAHEDRAL SYMMETRY AND THE
24-CELL 146 6.9 THE REGULAR POLYTOPES 150 7 THE IDEAL 155 7.1 DISCOVERY
AND INVENTION 156 7.2 DIVISION WITH REMAINDER 158 7.3 UNIQUE PRIME
FACTORIZATION 161 CONTENTS IX 7.4 GAUSSIAN INTEGERS 163 7.5 GAUSSIAN
PRIMES 166 7.6 RATIONAL SLOPES AND RATIONAL ANGLES 168 7.7 UNIQUE PRIME
FACTORIZATION LOST 169 7.8 IDEALS, OR UNIQUE PRIME FACTORIZATION
REGAINED 172 8 PERIODIC SPACE 177 8.1 THE IMPOSSIBLE TRIBAR 178 8.2 THE
CYLINDER AND THE PLANE 180 8.3 WHERE THE WILD THINGS ARE 183 8.4
PERIODIC WORLDS 185 8.5 PERIODICITY AND TOPOLOGY 187 8.6 A BRIEF HISTORY
OF PERIODICITY 190 9 THE INFINITE 197 9.1 FINITE AND INFINITE 198 9.2
POTENTIAL AND ACTUAL INFINITY 199 9.3 THE UNCOUNTABLE 201 9.4 THE
DIAGONAL ARGUMENT 203 9.5 THE TRANSCENDENTAL 205 9.6 YEARNING FOR
COMPLETENESS 208 EPILOGUE 211 INDEX \L4R TEUE^JU $. |
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| discipline | Mathematik |
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| index_date | 2024-07-02T15:24:59Z |
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| isbn | 156881254X 9781568812540 |
| language | English |
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| physical | XIII, 230 S. Ill., graph. Darst. |
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| spelling | Stillwell, John 1942- Verfasser (DE-588)128427264 aut Yearning for the impossible the surprising truths of mathematics John Stillwell Wellesley, Mass. Peters 2006 XIII, 230 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Recreações matemáticas larpcal Geschichte Mathematik Mathematics Mathematics History Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014940213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stillwell, John 1942- Yearning for the impossible the surprising truths of mathematics Recreações matemáticas larpcal Geschichte Mathematik Mathematics Mathematics History Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037944-9 |
| title | Yearning for the impossible the surprising truths of mathematics |
| title_auth | Yearning for the impossible the surprising truths of mathematics |
| title_exact_search | Yearning for the impossible the surprising truths of mathematics |
| title_exact_search_txtP | Yearning for the impossible the surprising truths of mathematics |
| title_full | Yearning for the impossible the surprising truths of mathematics John Stillwell |
| title_fullStr | Yearning for the impossible the surprising truths of mathematics John Stillwell |
| title_full_unstemmed | Yearning for the impossible the surprising truths of mathematics John Stillwell |
| title_short | Yearning for the impossible |
| title_sort | yearning for the impossible the surprising truths of mathematics |
| title_sub | the surprising truths of mathematics |
| topic | Recreações matemáticas larpcal Geschichte Mathematik Mathematics Mathematics History Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Recreações matemáticas Geschichte Mathematik Mathematics Mathematics History |
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