The geometric interpretation of quaternion and Octanion 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?

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.