Tiling with rectangles

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A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of $1 \times 2$ side ratio. The tilings with straight polyominoes of shapes such as $1 \times 3$ , $1 \times 4$ and tilings with polyominoes of shapes such as $2 \times 3$ 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]

Notes

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

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[x-1] 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

[1]

[2]

Congruent rectangles

Tilings with non-congruent rectangles

See also

Notes