Pi - unleashed: with CD-ROM
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
2001
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 270 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 3540665722 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804133404208267264 |
|---|---|
| adam_text | JORG ARNDT CHRISTOPH HAENEL PI - UNLEASHED TRANSLATED FROM THE GERMAN BY
CATRIONA AND DAVID LISCHKA WITH CD-ROM SPRINGER CONTENTS 1. THE STATE OF
PI ART 1 2. HOW RANDOM IS TT? 21 2.1 PROBABILITIES 21 2.2 IS 7 T NORMAL?
21 2.3 SO IS TT NOT NORMAL? 24 2.4 THE 163 PHENOMENON 25 2.5 OTHER
STATISTICAL RESULTS 28 2.6 THE INTUITIONISTS AND TT 30 2.7
REPRESENTATION OF CONTINUED FRACTIONS 32 3. SHORTCUTS TO TT 35 3.1
OBSCURER APPROACHES TO T T 35 3.2 SMALL IS BEAUTIFUL 37 3.3 SQUEEZING TT
THROUGH A SIEVE 38 3.4 TT AND CHANCE (MONTE CARLO METHODS) 39 3.5
MEMORABILIA 44 3.6 BIT FOR BIT 47 3.7 REFINEMENTS 49 3.8 THE TT ROOM IN
PARIS 50 4. APPROXIMATIONS FOR TT AND CONTINUED FRACTIONS 51 4.1
RATIONAL APPROXIMATIONS 51 4.2 OTHER APPROXIMATIONS 55 4.3 YOUTHFUL
APPROXIMATIONS 63 4.4 ON CONTINUED FRACTIONS 64 5. ARCUS TANGENS 6 9 5.1
JOHN MACHIN S ARCTAN FORMULA 69 5.2 OTHER ARCTAN FORMULAE 72 X CONTENTS
6. SPIGOT ALGORITHMS 77 6.1 THE SPIGOT ALGORITHM IN DETAIL 78 6.2
SEQUENCE OF OPERATIONS 80 6.3 A FASTER VARIANT 82 6.4 SPIGOT ALGORITHM
FOR E 84 7. GAUSS AND TT 87 7.1 THE TT AGM FORMULA 87 7.2 THE GAUSS AGM
ALGORITHM 90 7.3 SCHONHAGE VARIANT 92 7.4 HISTORY OF A FORMULA 94 8.
RAMANUJAN AND TT 103 8.1 RAMANUJAN S SERIES 103 8.2 RAMANUJAN S UNUSUAL
BIOGRAPHY 105 8.3 IMPULSES 110 9. THE BORWEINS AND TT 113 10. THE BBP
ALGORITHM 117 10.1 BINARY MODULO EXPONENTIATION 120 10.2 A C PROGRAM ON
THE BBP SERIES 123 10.3 REFINEMENTS 126 11. ARITHMETIC 131 11.1
MULTIPLICATION 131 11.2 KARATSUBA MULTIPLICATION 132 11.3 FFT
MULTIPLICATION 135 11.4 DIVISION 145 11.5 SQUARE ROOT 146 11.6 NTH ROOT
149 11.7 SERIES CALCULATION 150 12. MISCELLANEOUS 153 12.1 A TT QUIZ 153
12.2 LET NUMBERS SPEAK 154 12.3 A PROOF THAT TT = 2 155 12.4 THE BIG
CHANGE 155 12.5 ALMOST BUT NOT QUITE 156 12.6 WHY ALWAYS MORE? 158
CONTENTS XI 12.7 TT AND HYPERSPHERES 158 12.8 VIETE X WALLIS = OSIER 160
12.9 SQUARING THE CIRCLE WITH HOLES 162 12.10AN (IN)FINITE FUNNEL 164
13. THE HISTORY OF TT 165 13.1 ANTIQUITY 167 13.2 POLYGONS 170 13.3
INFINITE EXPRESSIONS 185 13.4 HIGH-PERFORMANCE ALGORITHMS 198 13.5 THE
HUNT FOR SINGLE TT DIGITS 203 TABLE: HISTORY OF TT IN THE PRE-COMPUTER
ERA 205 TABLE: HISTORY OF TT IN THE COMPUTER ERA 206 TABLE: HISTORY OF
DIGIT EXTRACTION RECORDS 207 14. HISTORICAL NOTES 209 14.1 THE EARLIEST
SQUARING THE CIRCLE IN HISTORY? 209 14.2 A TT LAW 211 14.3 THE
BIEBERBACH STORY 213 15. THE FUTURE: TT CALCULATIONS ON THE INTERNET 215
15.1 THE BINSPLIT ALGORITHM 215 15.2 THE TT PROJECT ON THE INTERNET 219
16. 7T FORMULA COLLECTION 223 17. TABLES 239 17.1 SELECTED CONSTANTS TO
100 PLACES (BASE 10) 239 17.2 DIGITS 0 TO 2,500 OF TT (BASE 10) 240 17.3
DIGITS 2,501 TO 5,000 OF TT (BASE 10) 241 17.4 DIGITS 0 TO 2,500 OF TT
(BASE 16) 242 17.5 DIGITS 2,501 TO 5,000 OF TT (BASE 16) 243 17.6
CONTINUED FRACTION ELEMENTS 0 TO 1,000 OF TT 244 17.7 CONTINUED FRACTION
ELEMENTS 1,001 TO 2,000 OF VR 245 A. DOCUMENTATION FOR THE HFLOAT
LIBRARY 247 A.I WHAT HFLOAT IS (GOOD FOR) 247 A.2 COMPILING THE LIBRARY
248 A.3 FUNCTIONS OF THE HFLOAT LIBRARY 248 A.4 USING HFLOATS IN YOUR
OWN CODE 250 XII CONTENTS A.5 COMPUTATIONS WITH EXTREME PRECISION 250
A.6 PRECISION AND RADIX 251 A.7 COMPILING & RUNNING THE 7R-EXAMPLE-CODE
253 A.8 STRUCTURE OF HFLOAT 253 A.9 ORGANISATION OF THE FILES 254 A. 10
DISTRIBUTION POLICY K, NO WARRANTY 255 BIBLIOGRAPHY 257 INDEX 265
|
| any_adam_object | 1 |
| author | Arndt, Jörg 1964- Haenel, Christoph |
| author_GND | (DE-588)142015806 |
| author_facet | Arndt, Jörg 1964- Haenel, Christoph |
| author_role | aut aut |
| author_sort | Arndt, Jörg 1964- |
| author_variant | j a ja c h ch |
| building | Verbundindex |
| bvnumber | BV019876811 |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)313836088 (DE-599)BVBBV019876811 |
| dewey-full | 516/.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.15 |
| dewey-search | 516/.15 |
| dewey-sort | 3516 215 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T20:08:10Z |
| institution | BVB |
| isbn | 3540665722 |
| language | English |
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| physical | XII, 270 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2001 |
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| publisher | Springer |
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| spelling | Arndt, Jörg 1964- Verfasser (DE-588)142015806 aut Pi - Algorithmen, Computer, Arithmetik Pi - unleashed with CD-ROM Jörg Arndt ; Christoph Haenel Berlin u.a. Springer 2001 XII, 270 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Algorithmus (DE-588)4001183-5 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Pi Zahl (DE-588)4174646-6 gnd rswk-swf 1\p (DE-588)4163417-2 Katalog gnd-content Pi Zahl (DE-588)4174646-6 s Algorithmus (DE-588)4001183-5 s 2\p DE-604 Arithmetik (DE-588)4002919-0 s 3\p DE-604 Haenel, Christoph Verfasser aut Parallele Sprachausgabe deutsch Pi HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013201026&sequence=000003&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Arndt, Jörg 1964- Haenel, Christoph Pi - unleashed with CD-ROM Algorithmus (DE-588)4001183-5 gnd Arithmetik (DE-588)4002919-0 gnd Pi Zahl (DE-588)4174646-6 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4002919-0 (DE-588)4174646-6 (DE-588)4163417-2 |
| title | Pi - unleashed with CD-ROM |
| title_alt | Pi - Algorithmen, Computer, Arithmetik |
| title_auth | Pi - unleashed with CD-ROM |
| title_exact_search | Pi - unleashed with CD-ROM |
| title_full | Pi - unleashed with CD-ROM Jörg Arndt ; Christoph Haenel |
| title_fullStr | Pi - unleashed with CD-ROM Jörg Arndt ; Christoph Haenel |
| title_full_unstemmed | Pi - unleashed with CD-ROM Jörg Arndt ; Christoph Haenel |
| title_short | Pi - unleashed |
| title_sort | pi unleashed with cd rom |
| title_sub | with CD-ROM |
| topic | Algorithmus (DE-588)4001183-5 gnd Arithmetik (DE-588)4002919-0 gnd Pi Zahl (DE-588)4174646-6 gnd |
| topic_facet | Algorithmus Arithmetik Pi Zahl Katalog |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013201026&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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