This is a paper that started with a question about how accurately I could measure curves drawn with drating tools and that quickly went off the rails when I found not just a physical limit due to my inability to manipulate the drafting tool but a hardset theoretical limit due to the mathemics being used to measure the line by me. I then investigated why those limits were imposed by the prefered tradesman type framework I wanted to use and what the upper limit on this acuracy was. Hence the theorem found which may be farmiliar to members of the mathematical community but has as of yet not been stated in the literature so far as I know. Drafting tools and and the non specialist mathematical framework this is framed in wil hopefully make this an enjoyable read to many types of readers.
mills michael (Sat,) studied this question.