A limited world

There is an interesting theorem in mathematics that says that all standard geometrical constructions can be done using just compass alone (as opposed to a compass and a straight edge). Similarly, there is another theorem that says that the same can be achieved using a straight edge alone, provided you have a fixed cirle, drawn in the plane, to start with. (Of course, in either case you'll need the pencil too :-) )

Thus, if the straight-edge was never invented people would still be able to do (Euclidean) geometry - making a compass is, of course, a lot easier than making a straight edge.

Which made me think - how was the first straight edge ever created?

Remember that there were no other measuring instruments to validate the straightness of the edge. Interestingly, this is a corollary to another classic problem in mecahnical engineering - how was the first plane surface made?

I have the (stock) answer to the latter problem, but I will post it in another article.

But the bottom line is, even in a limited world the ingenious mathematician will still be able to survive!