On unit circles which avoid all but two points of a given point-set (Q1348763)
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scientific article; zbMATH DE number 1740662
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On unit circles which avoid all but two points of a given point-set |
scientific article; zbMATH DE number 1740662 |
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On unit circles which avoid all but two points of a given point-set (English)
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25 March 2003
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The paper deals with an analogue of the following Gallai theorem of 1944, which solves the well-known Sylvester problem of 1893: For a finite set of at least two non-collinear points in a plane, there exists a line passing through exactly two of the points. The analogue concerns circles: Theorem. For any finite set of at least two points in the plane which has diameter less than \(\sqrt 3\), there is a unit circle passing through exactly two points of the set.
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finite set
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circle
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Sylvester problem
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