Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 878.68125
Autor: Erdös, Paul; Fishburn, Peter
Title: Minimum planar sets with maximum equidistance counts. (In English)
Source: Comput. Geom. 7, No.4, 207-218 (1997).
Review: Let g(k) be the smallest integer n for which there are n planar points each of which has k others equidistant from it. Every equilateral triangle realizes g(2) = 3. We prove that g(3) = 6, g(4) = 8 and g(5) \leq 16. Every realizer of g(3) = 6 consists of the vertices of two similarly-oriented equilateral triangles of side length d with distance d between each vertex of a triangle and its congruent twin in the other triangle. Our constructions for k = 4, 5 feature squares and equilateral triangles.
Classif.: * 68U05 Computational geometry, etc.
Keywords: minimum planar sets
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