Tiling with rectangles

A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of side
ratio. 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:

Stacked bond

Running bond

Basket weave

Herringbone pattern

Tilings with non-congruent rectangles

The smallest square that can be cut into rectangles, such that all m and n are different integers, is the 11 × 11 square, and the tiling uses five rectangles.
The smallest rectangle that can be cut into rectangles, such that all m and n are different integers, is the 9 × 13 rectangle, and the tiling uses five rectangles.