• DOI:10.4153/cmb-1967-014-0
• Corpus ID: 124281571

On Finite Plane Sets Containing for Every Pair of Points an Equidistant Point

@article{Brown1967OnFP,
  title={On Finite Plane Sets Containing for Every Pair of Points an Equidistant Point},
  author={W. G. Brown},
  journal={Canadian Mathematical Bulletin},
  year={1967},
  volume={10},
  pages={119 - 120}
}

• W. G. Brown
• Published 1 April 1967
• Mathematics
• Canadian Mathematical Bulletin

In [l] Melzak has posed the following problem: “A plane finite set Xn consists of n ≥ 3 points and contains together with any two points a third one, equidistant from them. Does Xn exist for every n ? Must it consist of points lying on some two concentric circles (one of which may reduce to a point)? How many distinct (that is, not similar) Xn are there for a given n ? …” We shall here provide a construction for uncountably many Xn for every n > 4, and a counterexample to the second question above.