Hurwitz quaternion order

A hurwitz quaternion order is like a rulebook that tells you how to play with special numbers called quaternions.

Imagine you have a set of blocks, but instead of just having one shape like regular blocks, these blocks can be arranged in different ways. Quaternions are like these special blocks. They have four parts, kind of like four sides of a block. And just like you can build different structures with different block shapes, you can use quaternions to do different things in math, like rotating objects in space.

But just like you have rules when playing with blocks, you also need rules when using quaternions. That's where the hurwitz quaternion order comes in. This "rulebook" tells you how to combine different quaternions together.

Think of it this way: in a board game, you have rules for moving pieces and taking turns. If you don't follow these rules, the game won't work properly. Similarly, if you don't follow the rules in the hurwitz quaternion order, the math won't work.

So, the hurwitz quaternion order helps you to make sure you're doing math with quaternions correctly, so that you can build cool structures and do fun things with them!