04/11/2011, 07:32 PM
I never heard about 3 dimensional numbers, the possible finite dimensional division algebras must have dimension 1 (real), 2 (complex), 4 (quaternion) or 8 (octonion), see wikipedia.
I remember that Hamilton tried to find to 3 dimensional numbers but failed, and came up in the end with quaternions.
Isnt that 4 dimensional, a,b,c,d?
How do you define division here?
I remember that Hamilton tried to find to 3 dimensional numbers but failed, and came up in the end with quaternions.
(04/06/2011, 04:20 PM)tommy1729 Wrote: it should be noted that there are 2 types of 3D numbers.
a + b P + c P^2 + d P^3 where 1 + P + P^2 + P^3 = 0 and P^4 = 1 and a , b , c , d are positive.
Isnt that 4 dimensional, a,b,c,d?
Quote:and the classical " 3D complex "
a + b w + c w^2 where a , b , c are real and w^3 = 1
How do you define division here?