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On Quaternions and Octonions : Their Geometry, Arithmetic, and Symmetry by Derek Smith, John Horton Conway, Derek A. Smith is a nonfiction available to read on EtoBox.

What is On Quaternions and Octonions : Their Geometry, Arithmetic, and Symmetry about?

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. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.

Who reads On Quaternions and Octonions : Their Geometry, Arithmetic, and Symmetry?

Author

Derek Smith, John Horton Conway, Derek A. Smith

Publisher

A K Peters/CRC Press

Published

2003

Language

EN

ISBN

9781000687774

Category

nonfiction

Subjects

Mathematics, Analysis, Stem

Rating

4 / 5 (20 ratings)

Updated

2026-03-14