The set of octonions, also sometimes called Cayley numbers and denoted , consists of the elements in a Cayley algebra. A typical octonion is of the form

where each of the triples , , , , , , behaves like the quaternions . Octonions are not associative. They have been used in the study of eight-dimensional space, in which a general rotation can be written as

Baez, J. C. "The Octonions." Bull. Amer. Math. Soc. 39, 145-205, 2002.

Conway, J. H. and Guy, R. K. "Cayley Numbers." In The Book of Numbers. New York: Springer-Verlag, pp. 234-235, 1996.

Conway, J. and Smith, D. On Quaternions and Octonions. Wellesley, MA: A K Peters, 2001.

Okubo, S. Introduction to Octonion and Other Non-Associative Algebras in Physics. New York: Cambridge University Press, 1995.

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1168, 2002.

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Weisstein, Eric W. "Octonion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Octonion.html