ip 85.171.202.183
vol 1
lock ********
title Hypercomplex Numbers: Quaternion, Octonion, Sedenian, and beyond
user strick
base r.1453442647000_18T

http://math.ucr.edu/home/baez/octonions/node5.html

https://orion.math.iastate.edu/jdhsmith/math/JS26jan4.htm

http://oas.uz.zgora.pl:7777/bib/bibwww.pdf?nIdA=14291&nIdSesji=-1


 http://english.stackexchange.com/questions/234607/what-comes-after-the-ducentiquinquagintasexions

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Quaternions (4-ions)
Octonions (8-ions)
Sedenions (16-ions)
Tricenibinions / trigintabinions (32-ions)
Sexageniquaternions / sexagintaquaternions (64-ions)
Centeniduodetricenions / centumduodetricenions (128-ions)
Duceniquinquagenisenions / ducentiquinquagintasenions (256-ions)

Quingeniduodenions / quingentiduodenions (512-ions)
Miliaviceniquaternions / millevigintiquaternions (1024-ions)
Binamiliaduodequinquagenions / duomiliaduodequinquagenions (2048-ions)
Quaternamilianonagenisenions / quattuormilianonagintasenions (4096-ions)
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https://ece.uwaterloo.ca/~dwharder/C++/CQOST/

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Cayley-Dickson Construction
First, we define the reals R where a ∈ R implies that a* = a. Given an algebra A of diminsion n, we create, using the Cayley-Dickson construction, an algebra of dimension 2n by taking pairs (a, b) ∈ A × A and thus define the standard operations:

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1 = (1, 0)
−(a, b) = (−a, −b)
(a, b)* = (a*, −b)
(a, b) + (c, d) = (a + c, b + d)
(a, b)(c, d) = (ac − d*b, da + bc*)
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In order to maintain a standard behaviour, a variation of the Cayley-Dickson construction shown in wikipedia is used for calculating products in higher dimensions. The justification is that it would be nice if the original quaternion identity ijk = -1 holds — the variation on wikipedia defines ijk = 1.
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https://en.wikipedia.org/wiki/Octonion

https://upload.wikimedia.org/wikipedia/commons/2/2d/FanoPlane.svg

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* /file FanoPlane.svg
* /file oct.pdf
* /file 0.pdf
* /file 0.html
* /imagefile 763419-candy-wallpaper.jpg
* /file 0.html
* /file 0.html
* /file