Date of Award
M.S. in Mathematics
Talmadge James Reid
More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit square.Here we consider various classes of tilings , this is, packings where there is no empty space inside the unit square. Several types of questions will be explored here. Various construction techniques are introduced, especially methods of generating tilings from tilings with fewer tiles. For some small values of n, I determine all tilings of the unit square with n tiles. I have found a best possible upper bound for a visible tiling, that is a tiling which every tile shares a face with the unit square. Furthermore, I generalize this result to higher dimensions for visible tilings.
Burt, John Randall, "(Visible) Tilings of Squares and Hypercubes" (2014). Electronic Theses and Dissertations. 1326.