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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



$n$-clusters for $1<n<7$

Authors: Landon Curt Noll and David I. Bell
Journal: Math. Comp. 53 (1989), 439-444
MSC: Primary 52A37
MathSciNet review: 970702
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Abstract: An n-cluster is a set of n lattice points in ${{\mathbf {R}}^2}$ with no 3 points collinear, no 4 points concyclic, and where all mutual distances are nonzero integers. The initial discoveries of n-clusters for $1 < n < 7$ are reported. A progress report on small 6-clusters and the search for a 7-cluster is described. A question on the impact of the lattice point restriction is raised, and the definition of n-cluster is generalized to ${{\mathbf {R}}^m}$.

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Article copyright: © Copyright 1989 American Mathematical Society