Convex nonagons with five intervertex distances |
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Authors: | Paul Erdös Peter Fishburn |
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Affiliation: | (1) Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364 Budapest, Hungary;(2) AT&T Bell Laboratories, 07974 Murray Hill, NJ, U.S.A. |
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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 n7, the samllest 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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Keywords: | 52C05 52C10 52B05 |
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