On Quaternions and Octonions [Hardcover]

John Horton Conway (Author), Derek Smith (Author)

Book Description

ISBN-10: 1568811349 | ISBN-13: 978-1568811345 | Publication Date: January 1, 2003 | Edition: 1st

This book investigates the geometry of the quaternion and octonion algebras. Following a comprehensive historical introduction, the special properties of 3- and 4-dimensional Euclidean spaces are illuminated 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 arithmetics of the quaternions and octonions are also described, and the book concludes with a new theory of octonion factorization. Topics covered include: - history - the geometry of complex numbers - quaternions and 3-dimensional groups - quaternions and 4-dimensional groups - the Hurwitz integral quaternions - the composition algebras - Moufang loops - octonions and 8-dimensional geometry - integral octonions - the octonion projective plane

Editorial Reviews

Review

" ""A resonant spike above background noise in one parameter as another parameter is varied is a frequent indicator…"" -Geoffrey Dixon, Mathematical Intelligencer , May 2004
""Those readers who are fascinated by the links between geometry and groups will find that this book gives them new insights. "" -Hugh Williams, The Mathematical Gazette , July 2004"

Product Details

• Hardcover: 159 pages
• Publisher: A K Peters/CRC Press; 1st edition (January 1, 2003)
• Language: English
• ISBN-10: 1568811349
• ISBN-13: 978-1568811345
• Product Dimensions: 9 x 6.1 x 0.6 inches
• Shipping Weight: 12.6 ounces (View shipping rates and policies)
• Average Customer Review: 3.4 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #140,545 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

59 of 66 people found the following review helpful:

3.0 out of 5 stars Good, but something is better, July 25, 2003

By 

Jim Curry (MT) - See all my reviews
(VINE VOICE)   

This review is from: On Quaternions and Octonions (Hardcover)

Conway is an excellent mathematician and an extremely lucid author. No criticism should be given to any of his writings. In the case of quaternions (and octonians), a much better, more complete, and more powerful view is achieved by seeing them in the larger setting of geometric algebra. The geometric algebra gives direct access to all the results and all the geometry of these algebras, and does so in an intuitive and useful way. I suggest that the new book by Chris Doran and Anthony Lasenby called "Geometric Algebra for Physicists" is a better place, generally, to get acquainted with these issues deeply. It isn't a criticism of Conway. It's just an advantage of seeing things in the right context.

2 of 3 people found the following review helpful:

3.0 out of 5 stars People either love Conway or hate him?, September 27, 2009

By 

R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: On Quaternions and Octonions (Hardcover)

This books gives a window into the newer notation in group theory.
Sometimes things that are "obvious" to Conway and his co-arthor,
just aren't to the rest of us.
But in contrast to that he gives concrete examples
of new approaches that are beyond classical Coexter
and Cartan type approaches.
If you are looking for physics applications to quantum mechanics
for modern group theory,
you might want to try another book,
but if you want an idea of what a Moufang loop is or why
octonions are not associative, then you might like this book.
Some time in this century we may even get
a chance to understand Freudenthal's metasymplectic geometry?
This book for me is sort of a study guide to
what i should try to learn for the future?

15 of 25 people found the following review helpful:

5.0 out of 5 stars A model of exposition, March 25, 2003

By 

Sally (London) - See all my reviews

This review is from: On Quaternions and Octonions (Hardcover)

John Conway's books are always well written, and this could serve as a model for other mathematics authors. I don't need to know that much about quaternions and octonions, but I found myself working through most of the book and the beautiful mathematics it covers. The only thing that disappoints is the dreadful cover and the difficulty getting hold of a copy in a bookstore. But then I guess Amazon.com exists to help people get their hands on stuff they might never see in a bookstore.