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.


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)


  • Books

  • Get in touch