# 2013 MAA Merten M. Hasse Prize for Expository Writing

Awards for exemplary writing in MAA journals and magazines were handed out in August at MAA MathFest in Hartford, Connecticut. The winning articles (PDF) are now available online, along with the award citations explaining why each article merited an award.

Merten M. Hasse Prize (presented to authors of a noteworthy expository paper appearing in an MAA publication, at least one of whose authors is a younger mathematician, generally under the age of 40)

Henryk Gerlach and Heiko von der Mosel
On Sphere-Filling Ropes
The American Mathematical Monthly, Vol. 118, no. 10, December 2011, pp. 863-876

Citation: In the paper “On Sphere-Filling Ropes,” authors Henryk Gerlach and Heiko von der Mosel address the problem of finding the longest closed curve of given positive minimal thickness of rope that covers the sphere. This is one of those rare articles that inspires the reader to ponder the details of solving a readily understood problem.

For each possible thickness of rope it was previously known that there is at least one length-maximizing curve, but the argument is not constructive. The authors present explicit solutions for a number of cases. Their initial construction involves a set of uniformly thick and pairwise disjoint horizontal circles covering the sphere. The sphere is cut by a vertical great circle, and then one side of the cut sphere is rotated in an attempt to form a single rope on the sphere by joining ends of those cut thick circles.

For a countable number of thicknesses, such ropes can be constructed, and they provide a solution to the problem. A uniqueness theorem shows that these solutions are the only solutions (up to rotations of the sphere) of the problem for each thickness.

The article includes a fine introduction that explains the problem in the context of other related problems and applications. The final section reviews the results and goes on to describe multiple open problems. In between the introduction and final section, there are helpful transitions between the main ideas, where the authors review what has been established and point out what will come next.

The mathematical ideas are clearly expressed and well organized. Figures throughout the paper greatly enhance the text.