Unification
(e1^e2)(e1^e2) = e1 e2 e1 e2 = -e1 e1 e2 e2 = -1
- Rotation by 90 degrees: e1(e1^e2)=e2
- Quaternions
- i=(e1^e2)
- j=(e2^e3)
- k=(e1^e3)
Then i^2=j^2=k^2=-1, ij=k, jk=i, ki=j
- Affine and Projective spaces
- Affine: embed in 1 higher dimensional Clifford space
- Projective: embed in 2 higher dimensional Clifford space
- Homogeneous coordinates