Earlier today, I was asked why a motion of the plane that fixes a line of points is called a reflection and I was stumped for an answer.
The best explanation I can think of is that the image of a shape under a reflection will be that shape's "mirror image" (this is mentioned on the Wikipedia page). If you look in a mirror, the image you see is a reflection of the real world. That said, in two dimensions terms like "flip" seem more intuitive.
This leads to my question:
- Where, historically, does the analogy of "reflection" arise in mathematics?