You know what’s surprising?

• ### Rotations are linear transformations.

I guess lo conocí but no entendí. Like, I could write you the matrix formula for a rotation by θ degrees:



But why is that linear? Lines are straight and circles bend. When you rotate something you are moving it along a circle. So how can that be linear?

I guess 2-D linear mappings ℝ²→ℝ² surprise our natural 1-D way of thinking about “straightness”.