# Perfect rectangle

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[[File: Schramm-Biermann Perfektes Rechteck 47x65.jpg |thumb|Perfect rectangle made of 10 squares in [concrete art](/source/concrete_art) (Image by the painter Irene Schramm-Biermann)]]
A '''perfect rectangle''' is a [rectangle](/source/rectangle) that can be divided into [square](/source/square)s of different sizes. If a perfect rectangle is specifically a square, it is analogously called a [perfect square](/source/squaring_the_square).

A rectangle that is not perfect is also called an '''imperfect rectangle'''.<ref>[https://mathworld.wolfram.com/PerfectRectangle.html Perfect rectangle] [Wolfram MathWorld](/source/Wolfram_MathWorld)</ref>

== Discoverers of Perfect Rectangles (Selection) ==
Many [mathematician](/source/mathematician)s have been involved in the discovery of perfect rectangles and perfect squares.

Below is a selection of important discoveries in this field.

* 1925: Zbigniew Moroń decomposed a perfect smallest possible 33x32 rectangle into nine squares.
* 1939: The [German](/source/Germans) mathematician [Roland Sprague](/source/Roland_Sprague) published a large perfect square with 55 squares.
* 1978: A. J. W. Duijvestijn dissected a perfect square into 21 squares with a total side length of 112, where 21 is the lowest possible number of subsquares of perfect squares.<ref>[https://mathworld.wolfram.com/PerfectSquareDissection.html Perfect Square Dissection] [Wolfram MathWorld](/source/Wolfram_MathWorld)</ref>

== Perfect Rectangles with Special Properties ==
Among the numerous perfect rectangles and squares, the following selected examples are intended to highlight some special features.<ref>[https://www.huybers.net/fit/rectangles.html Perfect rectangles]: an extensive collection of perfect rectangles</ref>

(The numbers in the squares indicate their respective side lengths.)

<gallery mode="packed" heights="160">
Perfektes Rechteck 33x32.svg|Smallest possible perfect rectangle (9 squares, Moroń)
Perfektes Rechteck 88x74.svg|Perfect rectangle with many squares (22 squares)
Perfektes Rechteck 113x98.svg|Almost symmetrical perfect rectangle (12 squares)
Perfektes Rechteck 115x69.svg|Elongated perfect rectangle (17 squares)
Perfektes Rechteck 105x104.svg|Perfect rectangle with a remarkably large side length of 7 for the smallest sub-square (10 squares)
Perfektes Quadrat 112x112.svg|Smallest possible simple perfect square (21 squares, Duijvestijn)
</gallery>

== References ==
<references />

== External links ==
* [https://www.maths2mind.com/schluesselwoerter/perfektes-rechteck Perfect Rectangle] Maths2Mind
* [https://www.michael-holzapfel.de/themen/rechtecke/bes_rechtecke.html Perfect Rectangle] Michael Holzapfel's Homepage
* [https://grundschullernportal.zum.de/wiki/Matheprojekte_der_Justus-Liebig-Universit%C3%A4t_Gie%C3%9Fen_f%C3%BCr_Grundsch%C3%BClerinnen_und_Grundsch%C3%BCler/Mathelexikon_WiSe_16_17/Rechteck "Did you know...?" (Perfect Rectangle)] Math projects from the [University of Giessen](/source/University_of_Giessen) for elementary school students
* [https://www.iread.it/perfect_rectangles.php Perfect Rectangles] Extensive collection of perfect rectangles on ''iread.it''

Category:Geometry

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Adapted from the Wikipedia article [Perfect rectangle](https://en.wikipedia.org/wiki/Perfect_rectangle) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Perfect_rectangle?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.