What are quaternions and ow can they be used?

[JungleJesus]

I've seen quaternions mentioned in a few articles online and I think they could be a very interesting subject. I would like to learn about them in simpler terms first. Can anyone give me the rundown on what they are and how they work?

 

[mgb_phys]

They are used as a way of describing a rotation around difference axis using matrix multiplication rather than trig and angles.
They probably have some deeper mathematical significance, but mostly they get used to work out how to rotate shapes in computer graphics.

http://en.wikipedia.org/wiki/Quaternions

 

[Mentallic]

I've heard that quaternions are an extension of the complex numbers. In the same way we had to invent complex numbers to solve all polynomials, quaternions had to be invented to... ?

edit: the wiki page kind of answers my question. I've yet quite been able to pinpoint exactly why complex numbers were unsatisfactory, and why quaternions were needed as an extension. Can these be considered as "super-complex" numbers in a way?

Note:

From the mid 1880s, quaternions began to be displaced by vector analysis, which had been developed by Josiah Willard Gibbs and Oliver Heaviside. Vector analysis described the same phenomena as quaternions, so it borrowed ideas and terms liberally from the classical quaternion literature. However, vector analysis was conceptually simpler and notationally cleaner, and eventually quaternions were relegated to a minor role in mathematics and physics.

However, quaternions have had a revival in the late 20th century, primarily due to their utility in describing spatial rotations. Representations of rotations by quaternions are more compact and faster to compute than representations by matrices...

 

[Tac-Tics]

I've seen quaternions mentioned in a few articles online and I think they could be a very interesting subject. I would like to learn about them in simpler terms first. Can anyone give me the rundown on what they are and how they work?

Quaternions are the real numbers when you add not one, but three complex units: i, j, k. The notable property is that multiplication doesn't commute: i * j = -j * i, and that i^2 = j^2 = k^2 = ijk.

They are used heavily in computer graphics. Quaternions are an alternate way to represent a rotation. The advantages they offer over matrices is that they take up less space in memory and you can compute rotations in fewer instructions with them. Additionally, given two quaternions, it's very easy to interpolate between them.

 

[JungleJesus]

Thanks for the information. I'll keep looking around for more. If anybody has anything to add, please feel free to do so.