'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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