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Convex nonagons with five intervertex distances

✍ Scribed by Paul Erdös; Peter Fishburn

Publisher
Springer
Year
1996
Tongue
English
Weight
860 KB
Volume
60
Category
Article
ISSN
0046-5755

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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