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.[1][2]

See also

Notes

  1. ^ a b Madachy, Joseph S. (1998). "Solutions to Problems and Conjectures". Journal of Recreational Mathematics. 29 (1): 73. ISSN 0022-412X.
  2. ^ Herringbone Tiles on a Bathroom Wall
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