We show that a square-tiling of a p\_q rectangle, where p and q are relatively prime integers, has at least log 2 p squares. If q>p we construct a square-tiling with less than qรp+C log p squares of integer size, for some universal constant C.
Tiling the unit square with squares and rectangles
โ Scribed by Jim Owings
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 282 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let T be a bounded region in the Cartesian plane built from finitely many rectangles of the form [a 1 , a 2 )\_[b 1 , b 2 ), with a 1 <a 2 and b 1 <b 2 . We give a necessary and sufficient condition for T to be tilable with finitely many positive and negative squares.
The problem of finding polyominoes that tile rectangles has attracted a lot of attention; see [1] for an overview, and [2, 3] for more recent results. Several general families of such polyominoes are known, but sporadic examples seem to be scarce. Marshall [2, Fig. 9] gives a polyomino of rectangula