On quaternions and octonions : their geometry, arithmetic, and symmetry / John H. Conway [and] Derek A. Smith.
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries...
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Full Text (via ProQuest) |
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| Main Authors: | , |
| Other title: | Their geometry, arithmetic, and symmetry |
| Format: | eBook |
| Language: | English |
| Published: |
Natick, Mass. :
CRC Press,
[2003]
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| Subjects: |
MARC
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| 100 | 1 | |a Conway, John H. |q (John Horton) |1 https://id.oclc.org/worldcat/entity/E39PBJj4p9yb39QkgPGr4wMHG3 | |
| 245 | 1 | 0 | |a On quaternions and octonions : |b their geometry, arithmetic, and symmetry / |c John H. Conway [and] Derek A. Smith. |
| 246 | 3 | 0 | |a Their geometry, arithmetic, and symmetry |
| 264 | 1 | |a Natick, Mass. : |b CRC Press, |c [2003] | |
| 264 | 4 | |c ©2003. | |
| 300 | |a 1 online resource (xii, 159 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 149-152) and index. | ||
| 505 | 0 | 0 | |g I. |t The complex numbers ; |t Introduction -- |t Complex numbers and 2-dimensional geometry -- |g II. |t The quaternions ; |t Quaternions and 3-dimensional groups -- |t Quaternions and 4-dimensional groups -- |t The Hurwitz integral quaternions -- |g III. |t The octonions ; |t The composition algebras -- |t Moufang loops -- |t Octonions and 8-dimensional geometry -- |t The Octavian integers O -- |t Automorphisms and subrings of O -- |t Reading O mod 2 -- |t The octonian projective plane [doublestruck capital]O[italic capital]P². |
| 520 | |a This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Quaternions. | |
| 650 | 0 | |a Cayley numbers (Algebra) | |
| 650 | 7 | |a Quaternions |2 fast | |
| 650 | 7 | |a Cayley numbers (Algebra) |2 fast | |
| 650 | 7 | |a Algebra |2 fast | |
| 700 | 1 | |a Smith, Derek Alan, |d 1970- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjt8RyvmWtFr8gGfYmY4C3 | |
| 758 | |i has work: |a On quaternions and octonions (Text) |1 https://id.oclc.org/worldcat/entity/E39PCG463DQgkvD47xgC4wwDdP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Conway, John H. (John Horton) |t On Quaternions and Octonions. |d Natick : CRC Press, ©2003 |z 9781568811345 |
| 856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/ucb/detail.action?docID=3059500 |z Full Text (via ProQuest) |
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