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, f
Intervertex distances in convex polygons
✍ Scribed by Paul Erdös; Peter Fishburn
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 496 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0166-218X
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Examples are given of n vertex convex polygons for which the distances between a fixed vertex and the remaining vertices, visited in order, form a multi-modal function. We show that this function may have as many as n/2 modes, or local maxima. Further examples are given of n vertex convex polygons i
Fishburn, P.C. and J.A. Reeds, Unit distances between vertices of a convex polygon, Computational Geometry: Theory and Applications 2 (1992) 81-91. Many years ago Danzer resolved an open question of ErdGs by constructing a convex 9-gon, each vertex of which has the same distance to three other verti