Date of Award
1-1-2014
Document Type
Thesis
Degree Name
M.S. in Mathematics
Department
Mathematics
First Advisor
William Staton
Second Advisor
Talmadge James Reid
Third Advisor
Bing Wei
Relational Format
dissertation/thesis
Abstract
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.
Recommended Citation
Burt, John Randall, "(Visible) Tilings of Squares and Hypercubes" (2014). Electronic Theses and Dissertations. 1326.
https://egrove.olemiss.edu/etd/1326