Is there a branch of mathematics that would deal with the ideas like the following:
How would you coat a rectangular area in paint with a paintbrush that has a finite length less than the length of the rectangular area but an infinitely small width?
The answer to this problem would be (I'd imagine) to smoothly paint a stroke from one end of the region to the other, then repeat while moving the brush over until the surface is entirely coated.
Is there some branch of mathematics that deals with problems of this type? I wish I could be more specific but I am unaware of any terms to describe this type of problem.
Also, I am unaware of how I would even tag this question, since I don't know the terms or branches, any help there would be appreciated too!