Octonions

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This editable Main Article is under development and subject to a disclaimer.

[edit intro]

Octonions are a non-commutative and non-associative extension of the real numbers. They were were first discovered by John Graves, a friend of Sir William Rowan Hamilton who first described the related quaternions. Although Hamilton offered to publicize Graves discovery, it took Arthur Cayley to rediscover and publish in 1845, for this reason octonions are also known as Cayley Numbers.

## Contents

* 1 Definition & basic operations
* 2 Properties
* 3 Applications
* 4 See also
* 5 Related topics
* 6 References

## Definition & basic operations[edit]

The octonions, 𝕆, are a eight-dimensional normed division algebra over the real numbers.

𝕆={a0+∑i=17aiei|a1,…,a7∈ℝ}

## Properties[edit]

## Applications[edit]

## See also[edit]

* Cayley-Dickson construction

## Related topics[edit]

* Geometric Algebra
* Fano plane
* Quaternions

## References[edit]