Problem of the Week 1070

Straighten the Circle

It is easy to fill an open disk with open line segments that do not intersect: just use all the horizontal chords. Is it possible to fill a closed disk with closed line segments (having nonzero length) that do not intersect?

Source: Problem 1070 was used as a Problem of the Week a long time ago. It was in Joe Konhauser's files (and appeared in our MAA book Which Way Did the Bicycle Go?), but we do not know who originated it.

© Copyright 2007 Stan Wagon. Reproduced with permission.