[Geometric Algebra] I was simply trying to rotate the cube. But it seems I'm misunderstanding something about the Geometric Algebra.

How much of a rotation is x? 90 degrees? 180?

If it’s 90 degrees then that rotation has order 4 (you have to do it 4 times to get back to the place you started) not order 2.

So x4 = 1 (assuming we’re writing 1 for the ‘do nothing’ action) not x2 = 1 as you wrote.

In your working, you also seem to use a bit of a mess of notation. What does -1 mean in this context? Is it the opposite (negative) of the “do nothing” action? What does that mean?

It might serve you better to write the opposite rotation of x as x-1 . This makes it a little clearer.

Also, if it were true that x2 = 1 then it would logically follow that x = x-1 as you showed.

Does this make sense?

/r/learnmath Thread Parent