🚀 go-pugleaf

In article <1992Oct5.154211.21663@ecrc.de> micha@ecrc.de writes:
>In article 24242@access.usask.ca, choy@skorpio.usask.ca (I am a terminator.) writes:
>>How do you know that the line you draw is really straight? What
>>defines straightness?
>
>This is something I've been wondering about since a long time. Although we can
>make a circle as precise as we want, I think we cannot make a really
>precise straight line - every straight line is made from another one or from a tool
>that has been made using some older straight lines - so it all comes down to
>copying a line that has been made thousands years ago. Although we have precise
>instruments and tools, we can only make better and better lines (so that eventually
>the error is less than an atom, and we are there), but IMHO there is no
>process to create a straight line directly. Or is it?

The compass is nice because it works straight from the definition of a
circle, while a ruler, as you note, is not so nice since it does not
work from the definition of a straight line as the shortest path between
two points.  However, there is a machine that has been built which draws
straight lines "by definition."  Alas, I forget how it works.  Maybe
someone can remind us or reinvent it.  Of course this is not to say it
really is better than a good ruler but it is philosophically satisfying.
I seem to remember that it was built, not for practical reasons, but
just to show it could be done.  Back in the age of mechanical (as
opposed to electronic) ingenuity they did this sort of thing.  Some of
you may know how to built a device which will measure the area of a
shape if you trace the outline of the shape.  Others may enjoy figuring
it out.  Nothing electronic allowed!  Big clue: Green's theorem.
Disclaimer: I would have to figure out the details myself so don't ask....