Abstract
Here we establish a set of eight points in general position in the plane, i.e. no three on a line, no four on a circle, and they determine 7 distinct distances, so that, thei-th distance occursi times,i = 1, 2, ⋯, 7. The points are embedded in a triangular net, and the distances are not ordered by size or in any other way. We shall show that some known and unknown examples forn < 8 with the above properties may also be lattice points of a similar net.
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References
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Research (partially) supported by the Hungarian National Foundation for Scientific Research (OTKA) grant, no. 1808.
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Palásti, I. Lattice-point examples for a question of Erdős. Period Math Hung 20, 231–235 (1989). https://doi.org/10.1007/BF01848126
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DOI: https://doi.org/10.1007/BF01848126