Geodesic
On the sets of \(n\) points forming \(n+1\) directions
Cédric Pilatte1
1University of Mons (UMONS)
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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Let $S$ be a set of $n\geq 7$ points in the plane, no three of which are collinear. Suppose that $S$ determines $n+1$ directions. That is to say, the segments whose endpoints are in $S$ form $n+1$ distinct slopes. We prove that $S$ is, up to an affine transformation, equal to $n$ of the vertices of a regular $(n+1)$-gon. This result was conjectured in 1986 by R. E. Jamison.
DOI : 10.37236/8308
Classification : 52C10, 52C30, 52C35
Mots-clés : set of \(n\geq 7\) points in the plane, regular \((n+1)\)-gon

Cédric Pilatte  1

1 University of Mons (UMONS) 
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     journal = {The electronic journal of combinatorics},
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Cédric Pilatte. On the sets of \(n\) points forming \(n+1\) directions. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8308

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