Can anybody give me any useful link for the history of quaternion? The quaternion and Octanion are constructed but why other do not exist? What is the geometric interpretation of a quaternion?

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    $\begingroup$ See mathworld.wolfram.com/Quaternion.html $\endgroup$ – TheSimpliFire Oct 29 '17 at 9:11
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    $\begingroup$ Other(bilinear associative operation without zero divisors) do not exist(besides usual, complex, quaternion and octanion multiplications), because of the arguments coming from the characteristic classes. It could be a quite strong and technical machinery depending on your background. $\endgroup$ – Mihail Oct 29 '17 at 9:32

In the case of complex space we have two real perpendicular axex while in the case of Quaternion we have 2 complex axes and a quaternion is constructed basically by the multiplication of 2 complex numbers. Similarly octanions are constructed from quaternions. But geometrically it has been proved that no further such extension is possible.


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