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Journal of Geometry

, 110:10 | Cite as

Packing of odd squares revisited

  • Antal Joós
  • Vojtech Bálint
Article
  • 9 Downloads

Abstract

It is known that \(\sum \nolimits _{i =1}^\infty {1/ (2i+1)^2}={\pi ^2/8}-1\). We can ask what is the smallest \(\epsilon \ge 0\) such that all squares of sides 1 / 3, 1 / 5, 1 / 7,...can be packed into a rectangle of area \({\pi ^2/8}-1+\epsilon \). We show that the proof of Paulhus\('\) key Lemma for the best known result is false and we give new upper estimate \(\epsilon <4.43\times 10^{-10}\).

Keywords

Square packing Rectangle Smallest area 

Mathematics Subject Classification

52C15 52C20 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of DunaújvárosDunaújvárosHungary
  2. 2.University of ZilinaŽilinaSlovakia

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