Definitions for octonion
oc·to·nion

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1. octonionnoun

   A nonassociative extension of a quaternion.

WikipediaRate this definition:0.0 / 0 votes

1. Octonion

   In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface O or blackboard bold O {\displaystyle \mathbb {O} } . Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative. Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used. Octonions are related to exceptional structures in mathematics, among them the exceptional Lie groups. Octonions have applications in fields such as string theory, special relativity and quantum logic. Applying the Cayley–Dickson construction to the octonions produces the sedenions.

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1. Octonion

   In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold . There are only four such algebras, the other three being the real numbers R, the complex numbers C, and the quaternions H. The octonions are the largest such algebra, with eight dimensions, double the number of the quaternions from which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity, namely they are alternative. Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used. Despite this they have some interesting properties and are related to a number of exceptional structures in mathematics, among them the exceptional Lie groups. Additionally, octonions have applications in fields such as string theory, special relativity, and quantum logic. The octonions were discovered in 1843 by John T. Graves, inspired by his friend William Hamilton's discovery of quaternions. Graves called his discovery octaves. They were discovered independently by Arthur Cayley and are sometimes referred to as Cayley numbers or the Cayley algebra.

How to pronounce octonion?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say octonion in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of octonion in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of octonion in Pythagorean Numerology is: 6

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Octonion
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Octonion
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=octonion