Direction trees (Q1820788)
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scientific article; zbMATH DE number 3995709
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Direction trees |
scientific article; zbMATH DE number 3995709 |
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Direction trees (English)
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1987
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A direction tree for a finite set X of points in the plane is a tree T whose vertices are the points of X such that any two edges of T determine lines with different slopes. Ungar's theorem says that any n noncollinear points in the real affine plane determine at least different n-1 slopes among connecting lines. This note uses Ungar's theorem plus Hall's theorem on distinct representatives to prove the existence of a direction tree for any finite set of noncollinear points.
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direction tree
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Ungar's theorem
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Hall's theorem
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noncollinear points
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