A tiling with rectangles is a
tiling
Tiling may refer to:
*The physical act of laying tiles
*Tessellations
Computing
*The compiler optimization of loop tiling
* Tiled rendering, the process of subdividing an image by regular grid
*Tiling window manager
People
* Heinrich Sylvester ...
which uses
rectangles as its parts. The
domino tilings are tilings with rectangles of side
ratio. The tilings with straight
polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling.
Polyominoes have been used in po ...
es 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.
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.
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See also
* Squaring the square
Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the s ...
* Tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ge ...
* Tiling puzzle
Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps). Some tiling puzzles ask you to dissect a given sh ...
Notes
Tessellation
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