Tiling with rectangles explained

A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of sideratio. The tilings with straight polyominoes of shapes such as, and tilings with polyominoes of shapes such as fall also into this category.

Congruent rectangles

Some tiling of rectangles include:

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.^[2]

See also

• Squaring the square
• Tessellation
• Tiling puzzle

Notes and References

1. Madachy. Joseph S.. Solutions to Problems and Conjectures . Journal of Recreational Mathematics. 1998. 29. 1. 73. 0022-412X.
2. https://www.viapu.com/herringbone-pattern-in-interior/ Herringbone Tiles on a Bathroom Wall