The orchard visibility problem and some variants

  • Authors:

  • Clyde P. Kruskal

  • Affiliations:

  • University of Maryland at College Park, Department of Computer Science, College Park, MD 20742, USA

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2008

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Abstract

Imagine that you are standing at the center of a circular orchard, with trees centered at all of the lattice points except there is no tree at the origin itself (where you are standing). How large must the radius of the trees be in order to completely block your view (in every direction). Let R be the radius of the orchard, and r be the radius of the trees. It turns out that if R (the radius of the orchard) is an integer then you can see out if and only if r