School of Mathematics Seminars and Lectures
Fewest Pieces of Cake, and Isoperimetric Square
by Prof. Hyman Bass (University of Michigan, USA,)
Sunday, June 22, 2014
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-66 )
at Colaba Campus ( AG-66 )
Description |
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 |