# Is the Composition of Two Rotations another Rotation?

Is the composition of two rotations about the origin, for sure, another rotation? This might seem a straightforward question, in two dimensions at least. But a simple arm demonstration illustrates that the matter is far less clear in the three-dimensions.

In this three-part video I share the question, demonstrating the issue with my arm, give away the answer, and then, for those who are fully invested, give a discussion of the complete mathematics behind the matter.

Is the composition of two rotations about the origin, for sure, a rotation?

A written essay about all this appears here too.