Date & Time: Friday, July 04, 2014, 16:00-17:00.
Venue: Ramanujan Hall
Title: Fewest Pieces of Cake, and Isoperimetric Square Tilings of Rectangles
Speaker: Hyman Bass, University of Michigan
Abstract: Suppose that $ s $ students want to equally share $ c $ cakes. What is the smallest number of cake pieces,$ p(c, s) $, needed to achieve this fair distribution? We will derive a formula for $ p(c, s) $ and describe two different distribution schemes that achieve this. One of them is associated with a square tiling of a $ c \times s $ rectangle $ R $, and we shall see that this square tiling is “isoperimetric” in the sense that it has smallest “perimeter” among all square tilings of $ R $. I will describe a generalized version of this problem that is still open.