Tiling with rectangles: Difference between revisions

Revision as of 22:05, 9 January 2006

Latest revision as of 18:04, 23 May 2024

(25 intermediate revisions by 18 users not shown)

Line 1:

{{Short description | Rectangular tilings using various shapes of rectangles}}

A '''tiling with rectangles''' is a [[tesselation|tiling]] which uses rectangles as its parts.

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 × 2}} side

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

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

== Congruent rectangles ==

Some tiling of rectangles include:

{| class=wikitable

|-

|[[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]]

|}

== 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.<supref name="x">{{cite journal|last1=Madachy|first1=Joseph S.|title=Solutions to Problems and Conjectures |journal=Journal of Recreational Mathematics|date=1998|volume=29|issue=1|page=73|issn=0022-412X}}</supref>.<br>

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.<supref name="x" />1</supref>[https://www.viapu.com/herringbone-pattern-in-interior/ Herringbone Tiles on a Bathroom Wall]</ref>

==See also==

* [[Squaring the square]]

[[tiling]], [[tiling puzzle]]

* [[Tessellation]]

[[tiling]],* [[tilingTiling puzzle]]

==Notes==

{{reflist}}

{{Tessellation}}

[[Category:TilingTessellation]]

==Reference==

[[Category:Rectangular subdivisions]]

# [[Journal of Recreational Mathematics]], 28:1, p.64.

{{geometry-stub}}

[[Category:Tiling]]