Tiling with rectangles: Difference between revisions

Revision as of 17:01, 10 October 2016

Latest revision as of 18:04, 23 May 2024

(8 intermediate revisions by 4 users not shown)

Line 1:

{{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 × 2}} side

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

Line 15 ⟶ 16:

== 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.<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{{title missing|page=73|issn=0022-412X}}</ref>

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

==See also==

Line 30 ⟶ 31:

[[Category:Tessellation]]

[[Category:Rectangular subdivisions]]

{{geometry-stub}}