There is a funny history septernion that I will post about someday. Today I will talk Hamilton’s quaternions. They are also called hyper complex numbers and can be summarized by the formula below, which by the way, is in a plate in a bridge in Dublin. Quaternios expression is:

q =

The i, j and k part are the vector part, or imaginary.

### Properties

Multiplication is not COMMUTATIVE – yes the first to be discovered.

ij=k ji=−k

jk=i kj=−i

ki=j ik=−j

### Forgot

Quaternions, as well as part of Hamilton’s work was forgot specially because of the utilization of vectors representation actually.

### Revival

But recently quaternions were revived by describing spatial rotations! Yup! Forget vector representation haha.

### Suggestion

Well, my main suggestion if your interested is to learn it from [3], which explain with some details about quaternions for computer 3D graphic animation.

### Ref

[1]https://en.wikipedia.org/wiki/Quaternion

[2] http://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2008/ErikEkedahl/reportErikEkedahl.pdf

[3] https://www.3dgep.com/understanding-quaternions/