I have been thinking of this problem for a while now, but can’t seem to figure it out. We are all familiar with adding an image in a PowerPoint file, say for example, a square. We can rotate however we want and regardless of the angle, it always appears the same (as in no obvious scaling seen).

My question is related to Group Theory – whatever function or mapping is behind this rotation-action, it surely must be form a Group, right? I really want to figure out what the underlying mathematics behind this rotation is and if it could form a Group.

Any suggestions where I could start? I have been struggling with finding literature related to this topic, so would appreciate any ideas!

Thanks a lot!