A history of mathematical impossibility:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford, United Kingdom
Oxford University Press
[2022]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite [267]-278. - Index |
| Beschreibung: | xi, 284 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9780192867391 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV048807881 | ||
| 003 | DE-604 | ||
| 005 | 20241204 | ||
| 007 | t| | ||
| 008 | 230209s2022 xx a||| |||| 00||| eng d | ||
| 020 | |a 9780192867391 |c hbk |9 978-0-19-286739-1 | ||
| 035 | |a (OCoLC)1372477412 | ||
| 035 | |a (DE-599)BVBBV048807881 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-706 |a DE-83 |a DE-210 |a DE-188 |a DE-12 | ||
| 084 | |a HIST |q DE-210 |2 fid | ||
| 084 | |a SG 500 |0 (DE-625)143049: |2 rvk | ||
| 084 | |a SG 700 |0 (DE-625)143071: |2 rvk | ||
| 100 | 1 | |a Lützen, Jesper |e Verfasser |0 (DE-588)132955202 |4 aut | |
| 245 | 1 | 0 | |a A history of mathematical impossibility |c Jesper Lützen |
| 264 | 1 | |a Oxford, United Kingdom |b Oxford University Press |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a xi, 284 Seiten |b Illustrationen, Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis Seite [267]-278. - Index | ||
| 648 | 7 | |a Geschichte |2 gnd |9 rswk-swf | |
| 650 | 0 | 7 | |a Unmöglichkeit |g Philosophie |0 (DE-588)7700608-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Problem |0 (DE-588)4114530-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Mathematical analysis / History | |
| 653 | 0 | |a Mathematical analysis | |
| 653 | 6 | |a History | |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 1 | |a Unmöglichkeit |g Philosophie |0 (DE-588)7700608-2 |D s |
| 689 | 0 | 2 | |a Mathematisches Problem |0 (DE-588)4114530-6 |D s |
| 689 | 0 | 3 | |a Geschichte |A z |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |o 10.1093/oso/9780192867391.001.0001 |z 978-0-19-195947-9 |z 978-0-19-269303-7 |w (DE-604)BV048690626 |
| 856 | 4 | 2 | |m Digitalisierung Deutsches Museum |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034073885&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-034073885 | |
Datensatz im Suchindex
| _version_ | 1817529975219159040 |
|---|---|
| adam_text |
C
ONTENTS
1.
INTRODUCTION
1.1
THE ORGANIZATION OF THE BOOK
1.
2 WHAT IS AN IMPOSSIBILITY THEOREM?
1.
3 META STATEMENTS AND MATHEMATICAL RESULTS
1.
4 WHY ARE IMPOSSIBILITY RESULTS OFTEN MISUNDERSTOOD
A
MONG AMATEUR MATHEMATICIANS?
1.5 IMPOSSIBILITY RESULTS IN MATHEMATICS AND ELSEWHERE
1.
6 A CLASSIFICATION OF MATHEMATICAL IMPOSSIBILITY RESULTS
1.7 IMPOSSIBILITY AS A CREATIVE FORCE
2
. PREHISTORY: RECORDED AND NON-RECORDED IMPOSSIBILITIES
3
. THE FIRST IMPOSSIBILITY PROOF: INCOMMENSURABILITY
3.1 THE DISCOVERY
3
.2 THE CONSEQUENCES OF THE IMPOSSIBILITY THEOREM
3.3 INCOMMENSURABLE QUANTITIES IN EUCLID'S
ELEMENTS
4
. CLASSICAL PROBLEMS OF ANTIQUITY: CONSTRUCTIONS AND
POSITIVE THEOREMS
4.1 SQUARING A CIRCLE
4.2 DOUBLING THE CUBE
4
.3 TRISECTING THE ANGLE
1
1
4
5
6
9
1
2
1
3
1
5
1
9
1
9
2
3
25
2
7
28
3
5
39
V
5
. THE CLASSICAL PROBLEMS: THE IMPOSSIBILITY QUESTION IN ANTIQUITY 42
5.1 EXISTENCE AND CONSTRUCTABILITY 42
5
.2 PAPPUS ON THE CLASSIFICATION OF GEOMETRIC PROBLEMS 44
5
.3 THE QUADRATURE OF A CIRCLE 47
5
.4 USING NON-CONSTRUCTIBLE QUANTITIES: ARCHIMEDES AND PTOLEMY 48
6
. DIORISMS: CONCLUSIONS ABOUT THE GREEKS AND MEDIEVAL ARABS 52
6.1 DIORISMS
6
.2 CONCLUSION ON IMPOSSIBILITIES IN GREEK MATHEMATICS
6.3 MEDIEVAL ARABIC CONTRIBUTIONS
7
. CUBE DUPLICATION AND ANGLE TRISECTION IN THE
SEVENTEENTH AND EIGHTEENTH CENTURIES
7.1 THE SEVENTEENTH CENTURY
7.2 DESCARTES'S ANALYTIC GEOMETRY
7
.3 DESCARTES ON THE DUPLICATION OF A CUBE AND THE
TRISECTION OF AN ANGLE
5
2
56
59
6
5
65
66
6
9
X
CONTENTS
1
4. IMPOSSIBLE INTEGRALS
1
4.1 EARLY CONSIDERATIONS
1
4.2 ABEL'S MOSTLY UNPUBLISHED RESULTS
1
4.3 JOSEPH LIOUVILLE ON INTEGRATION IN ALGEBRAIC TERMS
1
4.4 LIOUVILLE ON INTEGRATION IN FINITE TERMS . DRATURE
14.5 LIOUVILLE ON SOLUTION OF DIFFERENTIAL EQUAT10NS BY QUA
1
4.6 LATER DEVELOPMENTS
1
4.7 CONCLUDING REMARKS ON THE SITUATION C.1830
1
5. IMPOSSIBILITY OF PROVING THE PARALLEL POSTULATE
1
5.1 THE AXIOMATIC DEDUCTIVE METHOD
1
5.2 THE PARALLEL POSTULATE AND THE ATTEMPTS TO PROVE IT
1
5.3 INDIRECT PROOFS: IMPLICIT NON-EUCLIDEAN GEOMETRY
1
5.4 NON-EUCLIDEAN GEOMETRY: THE INVENTION
1
5.5 THE HELP FROM DIFFERENTIAL GEOMETRY OF SURFACES
1
5.6. CONCLUSIONS
1
6. HILBERT AND IMPOSSIBLE PROBLEMS
1
6.1 IMPOSSIBILITY AS A SOLUTION; REJECTION OF
IGNORABIMUS
1
6.2 HILBERT'S THIRD PROBLEM: EQUIDECOMPOSABILITY
1
6.3 HILBERT'S SEVENTH PROBLEM
1
6.4 HILBERT'S FIRST PROBLEM
1
7. HILBERT AND GODEL ON AXIOMATIZATION AND INCOMPLETENESS
1
7.1 THE AXIOMATIZATION OF MATHEMATICS
1
7.2 HILBERT'S SECOND PARIS PROBLEM
1
7.3 THE FOUNDATIONAL CRISIS
1
7.4 GODELS INCOMPLETENESS THEOREMS
1
7.5 HILBERT'S TENTH PARIS PROBLEM
17.6 CONCLUSION
1
8. FERMAT'S LAST THEOREM
1
8.1 FERMAT'S CONTRIBUTION
1
8.2 NINETEENTH-CENTURY CONTRIBUTIONS
1
8.3 THE TWENTIETH-CENTURY PROOF
1
9. IMPOSSIBILITY IN PHYSICS
1
9.1 THE IMPOSSIBILITY OF PERPETUAL MOTION MACHINES
1
9.2 TWENTIETH-CENTURY IMPOSSIBILITIES IN PHYSICS
20
. ARROW'S IMPOSSIBILITY THEOREM
20.1 THE THEORY OF VOTING
20.2 WELFARE ECONOMICS
20.3 THE IMPOSSIBILITY THEOREM
20.4 THE GIBBARD-SATTERTHWAITE THEOREM
1
68
1
68
1
70
1
71
1
73
1
77
1
78
1
79
1
81
1
82
1
84
1
87
1
90
1
94
1
97
1
99
1
99
2
02
204
205
2
10
210
212
215
216
221
223
2
25
2
25
230
233
2
38
2
38
242
2
48
2
48
251
253
256
C
ONTENTS
XI
2
1. CONCLUSION 259
2
1.1 FROM UNIMPORTANT NON-RESULTS TO REMARKABLE "SOLUTIONS" 259
21.2 FROM META-STATEMENTS TO MATHEMATICAL THEOREMS 260
21.3 DIFFERENT TYPES OF PROBLEMS AND DIFFERENT TYPES OF PROOFS 260
21.4 PURE AND APPLIED IMPOSSIBILITY THEOREMS 262
2
1.5 CONTROVERSIES 263
2
1.6 IMPOSSIBILITY AS A CREATIVE FORCE 263
R
ECOMMENDED SUPPLEMENTARY READING
265
R
EFERENCES
267
I
NDEX
279
C
ONTENTS
IX
7
.4 DESCARTES'S CONTRIBUTIONS 74
7
.5 THE EIGHTEENTH CENTURY 75
7
.6 MONTUCLA AND CONDORCET COMPARED WITH DESCARTES 79
8
. CIRCLE QUADRATURE IN THE SEVENTEENTH CENTURY 81
8
.1 "SOLUTIONS" AND POSITIVE RESULTS 81
8
.2 DESCARTES ON THE QUADRATURE OF A CIRCLE 83
8
.3 WALLIS ON THE IMPOSSIBILITY OF AN ANALYTIC QUADRATURE OF
A CIRCLE 85
8
.4 DIFFERENT QUADRATURES OF A CIRCLE 89
8
.5 GREGORY ON IMPOSSIBILITY PROOFS AND THE NEW ANALYSIS 91
8.6 GREGORY'S ARGUMENT FOR THE IMPOSSIBILITY OF THE
ALGEBRAIC INDEFINITE CIRCLE QUADRATURE 93
8
.7 HUYGENS' AND WALLIS' CRITIQUE OF GREGORY 96
8
.8 LEIBNIZ ON THE IMPOSSIBILITY OF THE INDEFINITE CIRCLE QUADRATURE 99
8.9 NEWTON'S ARGUMENT FOR THE IMPOSSIBILITY OF THE
ALGEBRAIC INDEFINITE OVAL QUADRATURE 102
8
.10 WHY PROVE IMPOSSIBILITY 105
9
. CIRCLE QUADRATURE IN THE EIGHTEENTH CENTURY 108
9
.1 JOSEPH SAURIN (1659-1737) 108
9
.2 ANONYMOUS 110
9
.3 THOMAS FANTET DE LAGNY (1660-1734) 110
9
.4 THE ENLIGHTENED OPINION 112
9
.5 D'ALERNBERT 114
9
.6 THE FRENCH ACADEMY OF SCIENCES. CONDORCET 116
9
.7 ENLIGHTENING THE AMATEURS 117
9
.8 LAMBERT AND THE IRRATIONALITY OF
RE
118
IO
. IMPOSSIBLE EQUATIONS MADE POSSIBLE: THE COMPLEX NUMBERS 121
10.1 THE EXTENSION OF THE NUMBER SYSTEM: WALLIS'S ACCOUNT 121
10.2 CARDANOS SOPHISTICATED AND USELESS NUMBERS 124
10
.3 THE UNREASONABLE USEFULNESS OF THE COMPLEX NUMBERS 127
10.4 A DIGRESSION ABOUT INFINITESIMALS 130
1
1. EULER AND THE BRIDGES OF KONIGSBERG
1
2. THE INSOLVABILITY OF THE QUINTIC BY RADICALS
1
2.1 EARLY RESULTS
1
2.2 PAOLO RUFFINI
1
2.3 NIELS HENRIK ABEL
13
. CONSTRUCTIONS WITH RULER AND COMPASS: THE FINAL
I
MPOSSIBILITY PROOFS
13
.1 GAUSS ON REGULAR POLYGONS
13.2 WANTZCL
1
3.3 THE QUADRATURE OFA CIRCLE
13
3
1
40
1
40
1
45
1
49
1
55
1
55
1
60
1
63 |
| adam_txt | |
| any_adam_object | 1 |
| any_adam_object_boolean | |
| author | Lützen, Jesper |
| author_GND | (DE-588)132955202 |
| author_facet | Lützen, Jesper |
| author_role | aut |
| author_sort | Lützen, Jesper |
| author_variant | j l jl |
| building | Verbundindex |
| bvnumber | BV048807881 |
| classification_rvk | SG 500 SG 700 |
| ctrlnum | (OCoLC)1372477412 (DE-599)BVBBV048807881 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| era | Geschichte gnd |
| era_facet | Geschichte |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV048807881</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20241204</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">230209s2022 xx a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780192867391</subfield><subfield code="c">hbk</subfield><subfield code="9">978-0-19-286739-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1372477412</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV048807881</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-210</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-12</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">HIST</subfield><subfield code="q">DE-210</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SG 500</subfield><subfield code="0">(DE-625)143049:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SG 700</subfield><subfield code="0">(DE-625)143071:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lützen, Jesper</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)132955202</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A history of mathematical impossibility</subfield><subfield code="c">Jesper Lützen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford, United Kingdom</subfield><subfield code="b">Oxford University Press</subfield><subfield code="c">[2022]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2022</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xi, 284 Seiten</subfield><subfield code="b">Illustrationen, Diagramme</subfield><subfield code="c">24 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverzeichnis Seite [267]-278. - Index</subfield></datafield><datafield tag="648" ind1=" " ind2="7"><subfield code="a">Geschichte</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Unmöglichkeit</subfield><subfield code="g">Philosophie</subfield><subfield code="0">(DE-588)7700608-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematisches Problem</subfield><subfield code="0">(DE-588)4114530-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Mathematical analysis / History</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="653" ind1=" " ind2="6"><subfield code="a">History</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Unmöglichkeit</subfield><subfield code="g">Philosophie</subfield><subfield code="0">(DE-588)7700608-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Mathematisches Problem</subfield><subfield code="0">(DE-588)4114530-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Geschichte</subfield><subfield code="A">z</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="o">10.1093/oso/9780192867391.001.0001</subfield><subfield code="z">978-0-19-195947-9</subfield><subfield code="z">978-0-19-269303-7</subfield><subfield code="w">(DE-604)BV048690626</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung Deutsches Museum</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034073885&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-034073885</subfield></datafield></record></collection> |
| id | DE-604.BV048807881 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:29:26Z |
| indexdate | 2024-12-04T17:00:56Z |
| institution | BVB |
| isbn | 9780192867391 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034073885 |
| oclc_num | 1372477412 |
| open_access_boolean | |
| owner | DE-706 DE-83 DE-210 DE-188 DE-12 |
| owner_facet | DE-706 DE-83 DE-210 DE-188 DE-12 |
| physical | xi, 284 Seiten Illustrationen, Diagramme 24 cm |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Oxford University Press |
| record_format | marc |
| spelling | Lützen, Jesper Verfasser (DE-588)132955202 aut A history of mathematical impossibility Jesper Lützen Oxford, United Kingdom Oxford University Press [2022] © 2022 xi, 284 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite [267]-278. - Index Geschichte gnd rswk-swf Unmöglichkeit Philosophie (DE-588)7700608-2 gnd rswk-swf Mathematisches Problem (DE-588)4114530-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematical analysis / History Mathematical analysis History Mathematik (DE-588)4037944-9 s Unmöglichkeit Philosophie (DE-588)7700608-2 s Mathematisches Problem (DE-588)4114530-6 s Geschichte z DE-604 Erscheint auch als Online-Ausgabe 10.1093/oso/9780192867391.001.0001 978-0-19-195947-9 978-0-19-269303-7 (DE-604)BV048690626 Digitalisierung Deutsches Museum application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034073885&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lützen, Jesper A history of mathematical impossibility Unmöglichkeit Philosophie (DE-588)7700608-2 gnd Mathematisches Problem (DE-588)4114530-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)7700608-2 (DE-588)4114530-6 (DE-588)4037944-9 |
| title | A history of mathematical impossibility |
| title_auth | A history of mathematical impossibility |
| title_exact_search | A history of mathematical impossibility |
| title_exact_search_txtP | A history of mathematical impossibility |
| title_full | A history of mathematical impossibility Jesper Lützen |
| title_fullStr | A history of mathematical impossibility Jesper Lützen |
| title_full_unstemmed | A history of mathematical impossibility Jesper Lützen |
| title_short | A history of mathematical impossibility |
| title_sort | a history of mathematical impossibility |
| topic | Unmöglichkeit Philosophie (DE-588)7700608-2 gnd Mathematisches Problem (DE-588)4114530-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Unmöglichkeit Philosophie Mathematisches Problem Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034073885&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lutzenjesper ahistoryofmathematicalimpossibility |