  In this paper we will examine unions of oriented and non-oriented unit
squares in same plane and measure the ratio of perimeter to area of these
unions. In 1998, T. Keleti published the conjecture that this ratio never
exceeds 4. We outline the current state of research on this conjecture and give
two proofs of a special case. Finally, we explore the difficulties that arise
from using similar methods in the general case and examine properties of any
potential counterexample.
