Abstract
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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Sagols, F., Marín, R. (2009). The Inscribed Square Conjecture in the Digital Plane. In: Wiederhold, P., Barneva, R.P. (eds) Combinatorial Image Analysis. IWCIA 2009. Lecture Notes in Computer Science, vol 5852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10210-3_32
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DOI: https://doi.org/10.1007/978-3-642-10210-3_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10208-0
Online ISBN: 978-3-642-10210-3
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