Convex nonagons with five intervertex distances

P. Erdős, Peter Fishburn

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The vertices of a convex planar nonagon determine exactly five distances if and only if they are nine vertices of a regular 10-gon or a regular 11-gon. This result has important ties to related concerns, including the maximum number of points in the plane that determine exactly five distances and, for each n ≥ 7, the smallest t for which there exists a convex n-gon whose vertices determine t distances and are not all on one circle.

Original languageEnglish
Pages (from-to)317-332
Number of pages16
JournalGeometriae Dedicata
Volume60
Issue number3
Publication statusPublished - 1996

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Nonagon
n-gon
Tie
Circle
If and only if

Keywords

  • Convex nonagons
  • Erdös conjecture
  • Intervertex distances
  • Lattice theory

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Convex nonagons with five intervertex distances. / Erdős, P.; Fishburn, Peter.

In: Geometriae Dedicata, Vol. 60, No. 3, 1996, p. 317-332.

Research output: Contribution to journalArticle

Erdős, P & Fishburn, P 1996, 'Convex nonagons with five intervertex distances', Geometriae Dedicata, vol. 60, no. 3, pp. 317-332.
Erdős, P. ; Fishburn, Peter. / Convex nonagons with five intervertex distances. In: Geometriae Dedicata. 1996 ; Vol. 60, No. 3. pp. 317-332.
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