The dissection of rectangles into squares

1940/01/01 by Rachelle L. Brooks, Cedric A. B. Smith, A. H. Stone +1 · 7 citations
Computer Science · Engineering · Mathematics · Medicine · #Dissection (medical) #Least-squares function approximation #Mathematics #Medicine #Statistics #Surgery #VLSI and FPGA Design Techniques #graph theory and CDMA systems #semigroups and automata theory

paper · doi:10.1215/s0012-7094-40-00718-9

openalex publication_date 1940/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

We consider the problem of dividing a rectangle into a finite number of non-overlapping squares, no two of which are equal. A dissection of a rectangle R into a finite number n of non-overlapping squares is called a squaring of R of order n; and the n squares are the elements of the dissection. The term “elements” is also used for the lengths of the sides of the elements. If there is more than one element and the elements are all unequal, the squaring is called perfect, and R is a perfect rectangle.

Citations

• Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird

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