The circle conjecture for plane integral point sets in semi-general position
A plane integral point set is a finite set of points in the Euclidean plane whose pairwise distances are integers; it is in semi-general position when no three points are collinear. A set has minimum diameter when its diameter is minimal among plane integral point sets of the same cardinality.
Circle conjecture. The points of a plane integral point set in semi-general position are situated on a circle.
The paper notes that all known examples in semi-general position with minimum diameter lie on a common circle, and proves this structure for sets with at most points. The conjecture asserts the circle property in general.
References
Primary source
Sascha Kurz and Alfred Wassermann, “On the minimum diameter of plane integral point sets”, arXiv:0804.1307 (2008).
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