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Tilings of the square with similar rectangels

Abstract

LetR(u) denote the rectangle of sidesu and 1. We prove that the square can be decomposed into finitely many rectangles similar toR(u) if and only ifu is algebraic and each of its conjugates lies in the open half-plane Re(z)>0.

References

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Laczkovich, M., Szekeres, G. Tilings of the square with similar rectangels. Discrete Comput Geom 13, 569–572 (1995). https://doi.org/10.1007/BF02574063

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Keywords

  • Rational Coefficient
  • Discrete Comput Geom
  • Negative Real Part
  • Minimal Polynomial
  • Positive Real Part