  We consider the problem of fairly dividing a two dimensional heterogeneous
good among multiple players. Applications include division of land as well as
ad space in print and electronic media. Classical cake cutting protocols
primarily consider a one-dimensional resource, or allocate each player multiple
infinitesimally small "pieces". In practice, however, the two dimensional
\emph{shape} of the allotted piece is of crucial importance in many
applications (e.g. squares or bounded aspect-ratio rectangles are most useful
for building houses, as well as advertisements). We thus introduce and study
the problem of fair two-dimensional division wherein the allotted plots must be
of some restricted two-dimensional geometric shape(s). Adding this geometric
constraint re-opens most questions and challenges related to cake-cutting.
Indeed, even the elementary \emph{proportionality} fairness criteria can no
longer be guaranteed in all cases. In this paper we thus examine the
\emph{level} of proportionality that \emph{can} be guaranteed, providing both
impossibility results (for proportionality that cannot be guaranteed), and
algorithmic constructions (for proportionality that can be guaranteed). We
focus primarily on the case when the cake is a rectilinear polygon and the
allotted plots must be squares or bounded aspect-ratio rectangles.
