Tiling with rectangles: Difference between revisions

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{{Short description | Rectangular tilings using various shapes of rectangles}}
A '''tiling with rectangles''' is a [[tessellation|tiling]] which uses [[rectangle]]s as its parts. The [[Domino tiling|domino tilings]] are tilings with rectangles of {{math|1 X× 2}} side

ratio. The tilings with straight [[polyomino]]es of shapes likesuch as {{math|1 X× 3}}, {{math|1 X× 4}} and

tilings with polyominoes of shapes likesuch as {{math|2 X× 3}} fall also into this category.

== Congruent rectangles ==

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|[[File:Stacked bond.png|150px]]<br>Stacked bond

|[[File:Wallpaper group-cmm-1.jpg|150px]]<br>Running bond

|[[File:Wallpaper group-p4g-1.jpg|150px]]<br>[[Basketweave|Basket weave]]

|[[File:Basketweave bond.svg|150px]]<br>Basket weave

|[[File:Herringbone bond.svg|150px]]<br>[[Herringbone pattern]]

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== Tilings with non-congruent rectangles ==

The smallest square that can be cut into (m x× n) rectangles, such that all m and n are different integers, is the 11 x× 11 square, and the tiling uses five rectangles.<ref name="x">[[{{cite journal|last1=Madachy|first1=Joseph S.|title=Solutions to Problems and Conjectures |journal=Journal of Recreational Mathematics]], 28:|date=1998|volume=29|issue=1, p.64|page=73|issn=0022-412X}}</ref>

The smallest rectangle that can be cut into (m x× n) rectangles, such that all m and n are different integers, is the 9 x× 13 rectangle, and the tiling uses five rectangles.<ref name="x" /><ref>[https://www.viapu.com/herringbone-pattern-in-interior/ Herringbone Tiles on a Bathroom Wall]</ref>

==See also==

* [[Squaring the square]]

* [[tessellationTessellation]]

* [[tilingTiling puzzle]]

==Notes==

{{reflist}}

{{Tessellation}}

[[Category:Tessellation]]

[[Category:Rectangular subdivisions]]

{{geometry-stub}}