{{Multiple issues| {{more footnotes|date=January 2026}} {{Sources exist|date=April 2026}} }} [[File: Schramm-Biermann Perfektes Rechteck 47x65.jpg |thumb|Perfect rectangle made of 10 squares in concrete art (Image by the painter Irene Schramm-Biermann)]] A '''perfect rectangle''' is a rectangle that can be divided into squares of different sizes. If a perfect rectangle is specifically a square, it is analogously called a perfect square.
A rectangle that is not perfect is also called an '''imperfect rectangle'''.<ref>[https://mathworld.wolfram.com/PerfectRectangle.html Perfect rectangle] Wolfram MathWorld</ref>
== Discoverers of Perfect Rectangles (Selection) == Many mathematicians 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 mathematician 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</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 for elementary school students * [https://www.iread.it/perfect_rectangles.php Perfect Rectangles] Extensive collection of perfect rectangles on ''iread.it''
Category:Geometry