Extension - Describing 2D and 3D shapes

This is a thought provoking activity about how many variables are needed to describe a shape.

For example, if you don’t care about size, rotation or position all squares are the same.
To define size, one variable is needed.
To define rotation, one variable is needed.
To define position in the 2D plane, two variables are needed.

So to fully define any square requires four variables.
There are many possible different choices for these four.

(Updated 2023)