I have heard but not confirmed that one reason geometers seem to be obsessed with what can be constructed using a compass (for drawing circles) and a straight edge (for drawing lines) is that they used these to draw out the floor plans of cathederals and temples before beginning the construction.

Not using arbitrary lengths of measurement would free them to some extent from restrictions of scale, and cause them to focus on the pure geometry of logical proofs instead.

Euclid the (online) Game is a wonderful way to learn this logic by solving progressively harder puzzles using only these tools and others that you discover can be created from them.  Play the game if you want to see what I mean 🙂
Click here to play ~