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.