Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-08-04T05:57:55.633Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 November 2018

W.G. Brown
W.G. Brown*
Affiliation:
University of British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 119 - 120
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Melzak, Z. A., Problems connected with convexity. Canad. Math. Bull. 8 (1966), pages 565-573: Problem (21).CrossRefGoogle Scholar