Tales of Impossibility : : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / / David S. Richeson.
A comprehensive look at four of the most famous problems in mathematicsTales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straigh...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English |
---|---|
VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2019] ©2019 |
Year of Publication: | 2019 |
Language: | English |
Online Access: | |
Physical Description: | 1 online resource (456 p.) :; 163 b/w illus. 5 tables. |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9780691194233 |
---|---|
ctrlnum |
(DE-B1597)535141 (OCoLC)1110108642 |
collection |
bib_alma |
record_format |
marc |
spelling |
Richeson, David S., author. aut http://id.loc.gov/vocabulary/relators/aut Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / David S. Richeson. Princeton, NJ : Princeton University Press, [2019] ©2019 1 online resource (456 p.) : 163 b/w illus. 5 tables. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Contents -- Preface -- Introduction -- CHAPTER 1. The Four Problems -- CHAPTER 1. The Four Problems -- CHAPTER 3. Compass-and- Straightedge Constructions -- CHAPTER 4. The First Mathematical Crisis -- CHAPTER 5. Doubling the Cube -- CHAPTER 6. The Early History of π -- CHAPTER 7. Quadratures -- CHAPTER 8. Archimedes's Number -- CHAPTER 9. The Heptagon, the Nonagon, and the Other Regular Polygons -- CHAPTER 10. Neusis Constructions -- CHAPTER 11. Curves -- CHAPTER 12. Getting By with Less -- CHAPTER 13. The Dawn of Algebra -- CHAPTER 14. Viète's Analytic Art -- CHAPTER 15. Descartes's Compass-and- Straightedge Arithmetic -- CHAPTER 16. Descartes and the Problems of Antiquity -- CHAPTER 17. Seventeenth- Century Quadratures of the Circle -- CHAPTER 18. Complex Numbers -- CHAPTER 19. Gauss's 17-gon -- CHAPTER 20. Pierre Wantzel -- CHAPTER 21. Irrational and Transcendental Numbers -- EPILOGUE. Sirens or Muses? -- Notes -- References -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star A comprehensive look at four of the most famous problems in mathematicsTales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems-squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle-have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs-demonstrating the impossibility of solving them using only a compass and straightedge-depended on and resulted in the growth of mathematics.Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems.Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Mathematics, Ancient. MATHEMATICS / History & Philosophy. bisacsh Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English 9783110610765 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 9783110664232 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 English 9783110610406 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 9783110606362 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2019 9783110663365 print 9780691192963 https://doi.org/10.1515/9780691194233?locatt=mode:legacy https://www.degruyter.com/isbn/9780691194233 Cover https://www.degruyter.com/cover/covers/9780691194233.jpg |
language |
English |
format |
eBook |
author |
Richeson, David S., Richeson, David S., |
spellingShingle |
Richeson, David S., Richeson, David S., Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / Frontmatter -- Contents -- Preface -- Introduction -- CHAPTER 1. The Four Problems -- CHAPTER 3. Compass-and- Straightedge Constructions -- CHAPTER 4. The First Mathematical Crisis -- CHAPTER 5. Doubling the Cube -- CHAPTER 6. The Early History of π -- CHAPTER 7. Quadratures -- CHAPTER 8. Archimedes's Number -- CHAPTER 9. The Heptagon, the Nonagon, and the Other Regular Polygons -- CHAPTER 10. Neusis Constructions -- CHAPTER 11. Curves -- CHAPTER 12. Getting By with Less -- CHAPTER 13. The Dawn of Algebra -- CHAPTER 14. Viète's Analytic Art -- CHAPTER 15. Descartes's Compass-and- Straightedge Arithmetic -- CHAPTER 16. Descartes and the Problems of Antiquity -- CHAPTER 17. Seventeenth- Century Quadratures of the Circle -- CHAPTER 18. Complex Numbers -- CHAPTER 19. Gauss's 17-gon -- CHAPTER 20. Pierre Wantzel -- CHAPTER 21. Irrational and Transcendental Numbers -- EPILOGUE. Sirens or Muses? -- Notes -- References -- Index |
author_facet |
Richeson, David S., Richeson, David S., |
author_variant |
d s r ds dsr d s r ds dsr |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Richeson, David S., |
title |
Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / |
title_sub |
The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / |
title_full |
Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / David S. Richeson. |
title_fullStr |
Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / David S. Richeson. |
title_full_unstemmed |
Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / David S. Richeson. |
title_auth |
Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / |
title_alt |
Frontmatter -- Contents -- Preface -- Introduction -- CHAPTER 1. The Four Problems -- CHAPTER 3. Compass-and- Straightedge Constructions -- CHAPTER 4. The First Mathematical Crisis -- CHAPTER 5. Doubling the Cube -- CHAPTER 6. The Early History of π -- CHAPTER 7. Quadratures -- CHAPTER 8. Archimedes's Number -- CHAPTER 9. The Heptagon, the Nonagon, and the Other Regular Polygons -- CHAPTER 10. Neusis Constructions -- CHAPTER 11. Curves -- CHAPTER 12. Getting By with Less -- CHAPTER 13. The Dawn of Algebra -- CHAPTER 14. Viète's Analytic Art -- CHAPTER 15. Descartes's Compass-and- Straightedge Arithmetic -- CHAPTER 16. Descartes and the Problems of Antiquity -- CHAPTER 17. Seventeenth- Century Quadratures of the Circle -- CHAPTER 18. Complex Numbers -- CHAPTER 19. Gauss's 17-gon -- CHAPTER 20. Pierre Wantzel -- CHAPTER 21. Irrational and Transcendental Numbers -- EPILOGUE. Sirens or Muses? -- Notes -- References -- Index |
title_new |
Tales of Impossibility : |
title_sort |
tales of impossibility : the 2000-year quest to solve the mathematical problems of antiquity / |
publisher |
Princeton University Press, |
publishDate |
2019 |
physical |
1 online resource (456 p.) : 163 b/w illus. 5 tables. Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- Introduction -- CHAPTER 1. The Four Problems -- CHAPTER 3. Compass-and- Straightedge Constructions -- CHAPTER 4. The First Mathematical Crisis -- CHAPTER 5. Doubling the Cube -- CHAPTER 6. The Early History of π -- CHAPTER 7. Quadratures -- CHAPTER 8. Archimedes's Number -- CHAPTER 9. The Heptagon, the Nonagon, and the Other Regular Polygons -- CHAPTER 10. Neusis Constructions -- CHAPTER 11. Curves -- CHAPTER 12. Getting By with Less -- CHAPTER 13. The Dawn of Algebra -- CHAPTER 14. Viète's Analytic Art -- CHAPTER 15. Descartes's Compass-and- Straightedge Arithmetic -- CHAPTER 16. Descartes and the Problems of Antiquity -- CHAPTER 17. Seventeenth- Century Quadratures of the Circle -- CHAPTER 18. Complex Numbers -- CHAPTER 19. Gauss's 17-gon -- CHAPTER 20. Pierre Wantzel -- CHAPTER 21. Irrational and Transcendental Numbers -- EPILOGUE. Sirens or Muses? -- Notes -- References -- Index |
isbn |
9780691194233 9783110610765 9783110664232 9783110610406 9783110606362 9783110663365 9780691192963 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA22 |
callnumber-sort |
QA 222 R534 42019 |
url |
https://doi.org/10.1515/9780691194233?locatt=mode:legacy https://www.degruyter.com/isbn/9780691194233 https://www.degruyter.com/cover/covers/9780691194233.jpg |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
510 - Mathematics |
dewey-full |
510.93 |
dewey-sort |
3510.93 |
dewey-raw |
510.93 |
dewey-search |
510.93 |
doi_str_mv |
10.1515/9780691194233?locatt=mode:legacy |
oclc_num |
1110108642 |
work_keys_str_mv |
AT richesondavids talesofimpossibilitythe2000yearquesttosolvethemathematicalproblemsofantiquity |
status_str |
n |
ids_txt_mv |
(DE-B1597)535141 (OCoLC)1110108642 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2019 |
is_hierarchy_title |
Tales of Impossibility : The 2000-Year Quest to Solve the Mathematical Problems of Antiquity / |
container_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English |
_version_ |
1770176301433356288 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05899nam a22007455i 4500</leader><controlfield tag="001">9780691194233</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20210830012106.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">210830t20192019nju fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780691194233</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9780691194233</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)535141</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1110108642</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA22</subfield><subfield code="b">.R534 2019</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT015000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510.93</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Richeson, David S., </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Tales of Impossibility :</subfield><subfield code="b">The 2000-Year Quest to Solve the Mathematical Problems of Antiquity /</subfield><subfield code="c">David S. Richeson.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2019]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2019</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (456 p.) :</subfield><subfield code="b">163 b/w illus. 5 tables.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Introduction -- </subfield><subfield code="t">CHAPTER 1. The Four Problems -- </subfield><subfield code="t">CHAPTER 1. The Four Problems -- </subfield><subfield code="t">CHAPTER 3. Compass-and- Straightedge Constructions -- </subfield><subfield code="t">CHAPTER 4. The First Mathematical Crisis -- </subfield><subfield code="t">CHAPTER 5. Doubling the Cube -- </subfield><subfield code="t">CHAPTER 6. The Early History of π -- </subfield><subfield code="t">CHAPTER 7. Quadratures -- </subfield><subfield code="t">CHAPTER 8. Archimedes's Number -- </subfield><subfield code="t">CHAPTER 9. The Heptagon, the Nonagon, and the Other Regular Polygons -- </subfield><subfield code="t">CHAPTER 10. Neusis Constructions -- </subfield><subfield code="t">CHAPTER 11. Curves -- </subfield><subfield code="t">CHAPTER 12. Getting By with Less -- </subfield><subfield code="t">CHAPTER 13. The Dawn of Algebra -- </subfield><subfield code="t">CHAPTER 14. Viète's Analytic Art -- </subfield><subfield code="t">CHAPTER 15. Descartes's Compass-and- Straightedge Arithmetic -- </subfield><subfield code="t">CHAPTER 16. Descartes and the Problems of Antiquity -- </subfield><subfield code="t">CHAPTER 17. Seventeenth- Century Quadratures of the Circle -- </subfield><subfield code="t">CHAPTER 18. Complex Numbers -- </subfield><subfield code="t">CHAPTER 19. Gauss's 17-gon -- </subfield><subfield code="t">CHAPTER 20. Pierre Wantzel -- </subfield><subfield code="t">CHAPTER 21. Irrational and Transcendental Numbers -- </subfield><subfield code="t">EPILOGUE. Sirens or Muses? -- </subfield><subfield code="t">Notes -- </subfield><subfield code="t">References -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">A comprehensive look at four of the most famous problems in mathematicsTales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems-squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle-have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs-demonstrating the impossibility of solving them using only a compass and straightedge-depended on and resulted in the growth of mathematics.Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems.Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematics, Ancient.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / History & Philosophy.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2019 English</subfield><subfield code="z">9783110610765</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2019</subfield><subfield code="z">9783110664232</subfield><subfield code="o">ZDB-23-DGG</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE Mathematics 2019 English</subfield><subfield code="z">9783110610406</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE Mathematics 2019</subfield><subfield code="z">9783110606362</subfield><subfield code="o">ZDB-23-DMA</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press Complete eBook-Package 2019</subfield><subfield code="z">9783110663365</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691192963</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9780691194233?locatt=mode:legacy</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9780691194233</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/cover/covers/9780691194233.jpg</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-061040-6 EBOOK PACKAGE Mathematics 2019 English</subfield><subfield code="b">2019</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-061076-5 EBOOK PACKAGE COMPLETE 2019 English</subfield><subfield code="b">2019</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-066336-5 Princeton University Press Complete eBook-Package 2019</subfield><subfield code="b">2019</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="b">2019</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DMA</subfield><subfield code="b">2019</subfield></datafield></record></collection> |