We study the presumably unnecessary convexity hypothesis in a theorem of Chung et al. on perimeter-minimizing planar tilings by convex pentagons. We prove that the theorem holds without the convexity hypothesis in certain special cases, and we offer direction for further research.
Frank Morgan, Atwell Professor of Mathematics, Williams College
Ghang, Whan; Martin, Zane; and Waruhiu, Steven`
"Perimeter-minimizing Tilings by Convex and Non-convex Pentagons,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16
, Article 2.
Available at: http://scholar.rose-hulman.edu/rhumj/vol16/iss1/2