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'Das Wesen der Mathematik ist ihre Freiheit'
The Essence of the Mathematics is its freedom
Georg Cantor

‘Michele has left this strange world a little before me. This means nothing. People like us, who believe in physics, know that the distinction made between past, present and future is nothing more than a persistent, stubborn illusion.’
Albert Einstein, about death of his friend Michele Besso

personal notes of Renzo Diomedi

, then if n=3 =

,

properties:
and

and

, , , , the reciprocal of a is b and vice versa

then

, ,

,

=

its conjugate = its transpose

where ~ is the equivalence relation that identifies 2 points if they both lie on the same straight line passing through the origin

dot and cross prod.:

unit vector, rot.axis

where is parallel and is perpendicular to rotation axis

=1/4(-a-b-c+ai+ak+aj+bj+bk+bi+ck-cj+ci+ai+bi+ci+a+aj+ak+bk+bj-b-cj-ck+c+aj+bj+cj-ak-ai+a+b+bi+bk+ci-c-ck+ak+bk+ck+aj-a-ai-bi+b-bj+c+ci+cj)=

length =

unit q =
a 2PI/3 rotation permutes i,j,k

and rot.func.= 3 axes are permutated ciclically

geodesic eq.

..............................to be continued

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