The Dissection of Rectangles Into Squares

  • R. L. Brooks
  • C. A. B. Smith
  • A. H. Stone
  • W. T. Tutte
Part of the Modern Birkhäuser Classics book series (MBC)


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.


Normal Form Equilateral Triangle Open Plane Vertical Side Horizontal Side 
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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • R. L. Brooks
    • 1
  • C. A. B. Smith
    • 1
  • A. H. Stone
    • 1
  • W. T. Tutte
    • 1
  1. 1.Trinity College, Princeton UniversityCambridgeEngland

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