The number pi:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2004
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | X, 322 S. graph. Darst. |
| ISBN: | 0821832468 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV019354984 | ||
| 003 | DE-604 | ||
| 005 | 20041007 | ||
| 007 | t | ||
| 008 | 040804s2004 xxud||| |||| 00||| eng d | ||
| 010 | |a 2003063768 | ||
| 020 | |a 0821832468 |c acidfree paper |9 0-8218-3246-8 | ||
| 035 | |a (OCoLC)53434668 | ||
| 035 | |a (DE-599)BVBBV019354984 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 1 | |a eng |h fre | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-355 |a DE-634 |a DE-11 |a DE-188 |a DE-20 | ||
| 050 | 0 | |a QA484 | |
| 082 | 0 | |a 516.22 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 100 | 1 | |a Eymard, Pierre |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Autour du nombre pi <Engl.> |
| 245 | 1 | 0 | |a The number pi |c Pierre Eymard ; Jean-Pierre Lafon |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2004 | |
| 300 | |a X, 322 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Pi (Le nombre) | |
| 650 | 7 | |a Pi |2 gtt | |
| 650 | 7 | |a Teoria dos números |2 larpcal | |
| 650 | 4 | |a Pi | |
| 650 | 0 | 7 | |a Geschichte |0 (DE-588)4020517-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Pi |g Zahl |0 (DE-588)4174646-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Pi |g Zahl |0 (DE-588)4174646-6 |D s |
| 689 | 0 | 1 | |a Geschichte |0 (DE-588)4020517-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Lafon, Jean-Pierre |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-012818932 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804132786783649792 |
|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Measurement of the Circle 1
§1.1. Archimedes duplication method 1
§1.2. Some surfaces and volumes linked to the number n 9
§1.3. Gauss s circle problem 27
§1.4. Buffon s needle 34
Chapter 2. Wallis s Formula and Some Others 43
§2.1. Viete s infinite product 44
§2.2. General notes on infinite products 46
§2.3. Wallis s infinite product 48
§2.4. 1/7F and the game of heads or tails 50
§2.5. Stirling s equivalent 52
§2.6. The formula of Gregory and Leibniz 53
§2.7. A series for the inverse tangent due to Euler 55
§2.8. Other series and integrals to express ?r 56
§2.9. Formulae of Machin type 58
§2.10. On the equation | = arctan ^ + ¦ • • + arctan ^ 62
§2.11. Continued fractions for it 65
§2.12. The formula of Bailey, Borwein and Plouffe 79
Chapter 3. Euler, Euler Again, Always Euler 83
§3.1. The place of 7r and of e in an analysis course 83
v
§3.2. n and Fourier series 90
§3.3. Some proofs of the formula ^=1 ^ = f 93
§3.4. The dilogarithm function 97
§3.5. Asymptotic behaviour of the mean of certain arithmetic
functions 99
§3.6. The Bernoulli numbers in analysis 106
§3.7. The Gamma function 120
Chapter 4. Squaring the Circle 129
§4.1. Ruler and compass constructions 129
§4.2. Questions of irrationality 134
§4.3. Lambert s proof of irrationality 137
§4.4. A proof of the irrationality of C(2) and £(3) due to
F. Beukers 143
§4.5. Transcendental numbers 146
§4.6. Algebraic characterization of constructible numbers 153
§4.7. The transcendency of e and of it 168
§4.8. A measure of irrationality for tt 177
§4.9. Regular polygons 182
Chapter 5. n and Elliptic Integrals 195
§5.1. Elliptic integrals and lemniscate arcs 197
§5.2. The arithmetic geometric mean 205
§5.3. Algorithms for calculating integrals of the first and second
kind 208
§5.4. An algorithm for calculating the digits of n due to
the brothers Borwein 219
§5.5. Abel and division of the lemniscate 221
§5.6. From Jacobi to Ramanujan 237
§5.7. Pi and Ramanujan 243
§5.8. An overview of the proof by J. Borwein and P. Borwein 251
Chapter 6. Solutions to the Exercises 255
Exercises for Chapter 1 255
Exercises for Chapter 2 266
Exercises for Chapter 3 276
Exercises for Chapter 4 288
Exercises for Chapter 5 305
Bibliography 313
Index 319
|
| any_adam_object | 1 |
| author | Eymard, Pierre |
| author_facet | Eymard, Pierre |
| author_role | aut |
| author_sort | Eymard, Pierre |
| author_variant | p e pe |
| building | Verbundindex |
| bvnumber | BV019354984 |
| callnumber-first | Q - Science |
| callnumber-label | QA484 |
| callnumber-raw | QA484 |
| callnumber-search | QA484 |
| callnumber-sort | QA 3484 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)53434668 (DE-599)BVBBV019354984 |
| dewey-full | 516.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.22 |
| dewey-search | 516.22 |
| dewey-sort | 3516.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01766nam a2200481zc 4500</leader><controlfield tag="001">BV019354984</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20041007 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">040804s2004 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2003063768</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821832468</subfield><subfield code="c">acidfree paper</subfield><subfield code="9">0-8218-3246-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)53434668</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019354984</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">fre</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA484</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Eymard, Pierre</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Autour du nombre pi <Engl.></subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The number pi</subfield><subfield code="c">Pierre Eymard ; Jean-Pierre Lafon</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 322 S.</subfield><subfield code="b">graph. Darst.</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">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pi (Le nombre)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Pi</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Teoria dos números</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pi</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geschichte</subfield><subfield code="0">(DE-588)4020517-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Pi</subfield><subfield code="g">Zahl</subfield><subfield code="0">(DE-588)4174646-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Pi</subfield><subfield code="g">Zahl</subfield><subfield code="0">(DE-588)4174646-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Geschichte</subfield><subfield code="0">(DE-588)4020517-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lafon, Jean-Pierre</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=012818932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-012818932</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV019354984 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:58:22Z |
| institution | BVB |
| isbn | 0821832468 |
| language | English French |
| lccn | 2003063768 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012818932 |
| oclc_num | 53434668 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-634 DE-11 DE-188 DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-634 DE-11 DE-188 DE-20 |
| physical | X, 322 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | American Mathematical Society |
| record_format | marc |
| spelling | Eymard, Pierre Verfasser aut Autour du nombre pi <Engl.> The number pi Pierre Eymard ; Jean-Pierre Lafon Providence, RI American Mathematical Society 2004 X, 322 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Pi (Le nombre) Pi gtt Teoria dos números larpcal Pi Geschichte (DE-588)4020517-4 gnd rswk-swf Pi Zahl (DE-588)4174646-6 gnd rswk-swf Pi Zahl (DE-588)4174646-6 s Geschichte (DE-588)4020517-4 s 1\p DE-604 Lafon, Jean-Pierre Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Eymard, Pierre The number pi Pi (Le nombre) Pi gtt Teoria dos números larpcal Pi Geschichte (DE-588)4020517-4 gnd Pi Zahl (DE-588)4174646-6 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4174646-6 |
| title | The number pi |
| title_alt | Autour du nombre pi <Engl.> |
| title_auth | The number pi |
| title_exact_search | The number pi |
| title_full | The number pi Pierre Eymard ; Jean-Pierre Lafon |
| title_fullStr | The number pi Pierre Eymard ; Jean-Pierre Lafon |
| title_full_unstemmed | The number pi Pierre Eymard ; Jean-Pierre Lafon |
| title_short | The number pi |
| title_sort | the number pi |
| topic | Pi (Le nombre) Pi gtt Teoria dos números larpcal Pi Geschichte (DE-588)4020517-4 gnd Pi Zahl (DE-588)4174646-6 gnd |
| topic_facet | Pi (Le nombre) Pi Teoria dos números Geschichte Pi Zahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT eymardpierre autourdunombrepiengl AT lafonjeanpierre autourdunombrepiengl AT eymardpierre thenumberpi AT lafonjeanpierre thenumberpi |