**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.