'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
~ back ~