Alexander,
Many thanks for an excellent read. You have given me several new insights. I had not previously thought of the Clifford basis vectors as representing a plane. In retrospect, it is clear now since every vector has a plane that is normal to it. Also, I had not previously seen any advantage to Clifford over Hamilton. You have made me reconsider this. Setting i = (e2)(e3) still seems odd but at least I now understand the reason for it.
I wonder what you think of the following ... Euler's Equation is (e^i*theta) = cos(theta) i*sin(theta). It is possible to express the dot product of two vectors by using the cosine of the angle between them. It is possible to express the cross product of two vectors by using the sine of the angle between them. Therefore, if there are two arbitrary vectors that are restricted to the j-k plane, it is possible to construct Euler's Equation using these two vectors, and the complex i then does not appear in the right-hand side of Euler's Equation. Is this a simplified version of your Equation 3.2?
Beginning with your Equation 6.1, I see a connection between your paper and Dr. Klingman's paper since division by the absolute value normalizes the value to either plus or minus one. The un-numbered equation at the top of page 8 is also similar to part of Dr. Klingman's work.
The two step rotation is a little hard for me to visualize although I generally understand your meaning. A sketch would be very nice, but with so much happening it might simply be confusing.
Best Regards and Good Luck,
Gary Simpson