We consider generalizations of the honeycomb problem to the sphere S2 and seek the perimeter-minimizing partition into n regions of equal area. We provide a new proof of Masters' result that three great semicircles meeting at the poles at 120 degrees minimize perimeter among partitions into three equal areas. We also treat the case of four equal areas, and we prove under various hypotheses that the tetrahedral arrangement of four equilateral triangles meeting at 120 degrees minimizes perimeter among partitions into four equal areas.

Author Bio

I began this research in the 2006 NSF Williams College SMALL undergraduate research Geometry Group, advised by Professor Frank Morgan, and then focused on partitioning problems on the sphere in my senior thesis at Williams College, again advised by Professor Morgan. I am now with Teach for America in Chicago.