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"Unlocking Puzzling Polygons," by Ivars Peterson. Science News, 23 September 2000.
Polygons come in many shapes, some complex and intricately indented. If we think of a polygon as a chain of rigid rods connected to each other in two dimensions with flexible joints, can we find a way to unfurl the polygon into a convex shape, without ever letting the rods cross? It's not as easy as it sounds, particularly when the polygon has a saw-tooth boundary. Most who worked on the problem believed they would eventually find an example of a polygon that couldn't be unraveled in two dimensions, but no one ever came up with a stumper. Now the question is finally settled. Erik Demaine, a 19-year-old computer science graduate student, Robert Conelly of Cornell University, and Gunter Rote of the Free University of Berlin have proved that any polygon can be uncrinkled. While an aesthetically appealing result, it has also caught the attention of researchers in several fields, including robotics and genetics.
--- Ben Stein