Math 459, Senior Seminar
11/4/11
Name: Grace DeTore
Title: What L-shapes Are Able To Be Tiled With Squares?
Source: Chris Freiling, Robert Hunter, Cynthia Turner, Russell Wheeler, Tiling Square and
Anti Squares, The American Mathematical Monthly, Vol. 107, No. 3, (2000), 195-204
Senior Project Ideas:
1.) The article introduces the notion of tiling a polygon with squares, but suggests that other
shapes of tiles and of polygons would yield interesting and more complex results. For
example, consider if the squares had to be of uniform size, or if we used similar right
triangles to use as tiles. A useful starting point to this would be to look at proofs of the
tileability of rectangles, which has been proven in various ways.
2.) The authors reduced the original posed problem of which L-shapes can be tiled with
squares into a simplified version that allows us to consider squares and anti-squares,
declaring that the former is still an open question. They suggest that attempting to solve the
more general posed question would be an interesting and worthy pursuit.
3.) I did not go into detail about the article’s description for reversing the algorithm in order
to find a way to do the actual tiling, (if it is possible). Explore this algorithm for tiling and
try to find other ways to go about proving the tileability, including how those different
ways may yield unique tiling patterns.