Carpenter's rule problem

The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: Can a simple planar polygon be moved continuously to a position where all its vertices are in convex position, so that the edge lengths and simplicity are preserved along the way? A closely related problem is to show that any non-self-crossing polygonal chain can be straightened, again by a continuous transformation that preserves edge distances and avoids crossings.

Both problems were successfully solved by Connelly, Demaine & Rote (2003).

The problem is named after the multiple-jointed wooden rulers popular among carpenters in the 19th and early 20th centuries before improvements to metal tape measures made them obsolete.