The Inscribed Square Conjecture in the Digital Plane

@inproceedings{Sagols2009TheIS,
  title={The Inscribed Square Conjecture in the Digital Plane},
  author={F. Sagols and Ra{\'u}l Mar{\'i}n},
  booktitle={IWCIA},
  year={2009}
}
The Inscribed Square Conjecture has been open since 1911. It states that any plane Jordan curve J contains four points on a non-degenerate square. In this article we prove that the conjecture holds for digital simple closed 4-curves, and that it is false for 8-curves. The given proof is based on a theorem due to Stromquist. We also discuss some properties of simple closed 4-curves in the digital plane containing a single non-degenerate inscribed square. 
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