On Quaternions and Octonions (Hardcover)

by John Horton Conway (Author), Derek Smith (Author) "We suppose you understand the real numbers!..." (more)
Key Phrases: quaternion triplets, octonion projective plane, unit octonions, Lattice of Korkine (more...)

Editorial Reviews

Product Description
An investigation of the geometry of quaternion and octonion algebras, this book is intended for mathematicians, physicists, and crystallographers at any level--from undergraduate to professional--who are interested in the symmetries of low-dimensional space.

The book can also be used as a text for graduate courses in many mathematical fields, including geometry, group theory, algebra, and number theory.

A Selection of Topics Covered:
The geometry of complex numbers
Quaternions and 3-dimensional groups
Quaternions and 4-dimensional groups
The Hurwitz integral quaternions
Moufang loops
Octonions and 8-dimensional geometry
Integral octonions
The octonion projective plane

Product Details

• Hardcover: 159 pages
• Publisher: AK Peters; 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: 3.5 out of 5 stars See all reviews (4 customer reviews)
• Amazon.com Sales Rank: #439,176 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

49 of 56 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

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.

4 of 4 people found the following review helpful:

1.0 out of 5 stars moronians, April 23, 2009

By	reader - See all my reviews

If you want a good laugh take a look at chapter six
in this hastily compiled piece of trash. No one who
does not already understand the material on octonians
will be able to penetrate this unannotated formulary.
The same goes for the entire second half of the book.
[The first half is just a rehash of material so familiar
that there is no need to see it in print for the N+1 st time. ]
The only worthwhile entry here is the reference guiding
readers to John Baez's article on octonians which:
a) is available free online and
b) actually explains in a reader friendly way the
history, math, and applications involved.

The authors (not to mention editors) should be ashamed
at such a sloppy treatment of this rich and historically
interesting episode in mathematics.

11 of 19 people found the following review helpful:

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

By	Sally (Colorado) - See all my reviews

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.