Advertisement

String-Wrapped Rotating Disks

  • Joseph O’Rourke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

Abstract

Let the centers of a finite number of disjoint, closed disks be pinned to the plane, but with each free to rotate about its center. Given an arrangement of such disks with each labeled + or −, we investigate the question of whether they can be all wrapped by a single loop of string so that, when the string is taut and circulates, it rotates by friction all the ⊕-disks counterclockwise and all the ⊝-disks clockwise, without any string-rubbing conflicts. We show that although this is not always possible, natural disk-separation conditions guarantee a solution. We also characterize the hexagonal “penny-packing” arrangements that are wrappable.

Keywords

Span Tree Unit Disk Separation Condition Short Edge Disk Radius 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abellanas, M.: Conectando puntos: poligonizaciones y otros problemas relacionados. Gaceta de la Real Sociedad Matematica Española 11(3), 543–558 (2008)MathSciNetGoogle Scholar
  2. 2.
    Demaine, E.D., Demaine, M.L., Palop, B.: Conveyer-belt alphabet. In: Aardse, H., van Baalen, A. (eds.) Findings in Elasticity, pp. 86–89. Pars Foundation, Lars Müller Publishers (April 2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Joseph O’Rourke
    • 1
  1. 1.Smith CollegeNorthamptonUSA

Personalised recommendations