Two discrete versions of the Inscribed Square Conjecture and some related problems

@article{Sagols2011TwoDV,
  title={Two discrete versions of the Inscribed Square Conjecture and some related problems},
  author={F. Sagols and Ra{\'u}l Mar{\'i}n},
  journal={Theor. Comput. Sci.},
  year={2011},
  volume={412},
  pages={1301-1312}
}
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 two different discrete versions of this conjecture are introduced and proved. The first version is in the field of digital topology: it is proved that the conjecture holds for digital simple closed 4-curves, and that it is false for 8-curves. The second one is in the topological graph theory field: it is proved that any cycle of the… Expand
5 Citations

Paper Mentions

AN INTEGRATION APPROACH TO THE TOEPLITZ SQUARE PEG PROBLEM
  • T. Tao
  • Mathematics
  • Forum of Mathematics, Sigma
  • 2017
  • 16
  • PDF
A survey on the Square Peg Problem
  • 38
  • Highly Influenced
  • PDF
Quadrilaterals inscribed in convex curves
  • 9
  • PDF

References

SHOWING 1-10 OF 17 REFERENCES
The Inscribed Square Conjecture in the Digital Plane
  • 6
INSCRIBED SQUARES IN PLANE CURVES
  • 27
  • PDF
Inscribed squares and square-like quadrilaterals in closed curves
  • 32
  • Highly Influential
Finite sets on curves and surfaces
  • 19
Old And New Unsolved Problems In Plane Geometry And Number Theory
  • 162
  • Highly Influential
Arcs and Curves in Digital Pictures
  • 142
Digital Topology
  • 233
  • PDF
Digital Geometry
  • 232
The discrete square peg problem
  • 15
  • PDF
...
1
2
...