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.
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.
Subsequently, to their work, Ileana Streinu provided a simplified combinatorial proof formulated in the terminology of robot arm motion planning.
Essentially, this folding process is a time-reversed version of the problem of convexifying a polygon of length smaller than π, but on the surface of a sphere rather than in the Euclidean plane.
This research, performed while he was still a high school student, won the second-place prize for Pardon in the 2007 Intel Science Talent Search (Cunningham 2007).