A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of 1 × 2 side ratio. The tilings with straight polyominoes of shapes such as 1 × 3, 1 × 4 and tilings with polyominoes of shapes such as 2 × 3 fall also into this category.
Congruent rectangles
Some tiling of rectangles include:
| Stacked bond | Running bond | Basket weave | Basket weave | Herringbone pattern |
Tilings with non-congruent rectangles
The smallest square that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 11 × 11 square, and the tiling uses five rectangles.1
The smallest rectangle that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 9 × 13 rectangle, and the tiling uses five rectangles.23
See also
Notes
References
Madachy, Joseph S. (1998). "Solutions to Problems and Conjectures". Journal of Recreational Mathematics. 29 (1): 73. ISSN 0022-412X. /wiki/ISSN_(identifier) ↩
Madachy, Joseph S. (1998). "Solutions to Problems and Conjectures". Journal of Recreational Mathematics. 29 (1): 73. ISSN 0022-412X. /wiki/ISSN_(identifier) ↩
Herringbone Tiles on a Bathroom Wall https://www.viapu.com/herringbone-pattern-in-interior/ ↩