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.