We had to start with something, might as well be that. Geometry is a lot more fun and interesting than algebra. It is hard to manipulate functions via rigid translations without understanding what they are, and it is hard to understand what they are without literally seeing what is happening. We aren’t starting with geometric view, we’re starting with the analytic view.
An introduction to the ideas of rigid translations.
For these reasons we will start out our work on rigid translations with some geometric descriptions and depictions. Once we have firmly established what is (and is not) a rigid translation intuitively, we will delve into the analytic mechanics of how to write and/or manipulate functions with rigid translations.
We will start with a geometric view of rigid translations because