Sorry to spoil the party, but this is the old 19th century way of teaching quaternions (and also complex numbers). It is much easier to start with some https://en.wikipedia.org/wiki/Group_theory and then you understand that quaternions are simply matrices of a specific form: https://en.wikipedia.org/wiki/Quaternion#Matrix_representati... . Quaternion multiplication is simply matrix multiplication of these matrices. And that's it. No mysteries, this is just simple linear algebra (you do't even need complex numbers, the real representation is enough and makes the connection to 4d rotations manifest).

In case you missed it, 3B1B has a brilliant video introducing quaternions: https://youtu.be/d4EgbgTm0Bg

Possibly off-topic: why does practically any description of quaternions include the anecdote about somebody carving something into some bridge in Ireland?

I’ve learned about plenty of mathematical concepts while having no idea who discovered them or under what circumstances. Why are quaternions the exception?

Dual quaternion are even whackier. They are the best formalism for reasoning about 3D space developing over time.

Here’s a cool example http://www.chinedufn.com/dual-quaternion-shader-explained/

Previous discussion

https://news.ycombinator.com/item?id=7364442

Those who like to have a print version:

https://github.com/frankMilde/interesting-reads/blob/master/...

I remember being introduced to quaternions recently by this post[0] which recommended this book[1].

[0]: https://www.haroldserrano.com/blog/best-books-to-develop-a-g...

[1]: https://www.amazon.com/Quaternions-Computer-Graphics-John-Vi...

I had a question about quaternions: does anyone use them for anything else than multiplying a rotation by a scalar?

In particular, it feels a bit like a waste of coding space to always use unit ones.

Anyone know an easy way to show that multiplication by a unit quaternion is a unitary operator?

I found these videos very helpful: https://www.youtube.com/watch?v=SCbpxiCN0U0

Protip: learn Geometric Algebra.

Please use Lie Groups/Algebra instead.

left handed thingies. go to geometric algebra for the real meal deal.

I have no idea why they insist on using such horrible graphs to explain a simple idea.

Go to wiki/quaternions. scroll down to about 2/3rds of the way ;)