Covering a triangle with sequences of its homothetic copies (Q1125607)
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scientific article; zbMATH DE number 1376171
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Covering a triangle with sequences of its homothetic copies |
scientific article; zbMATH DE number 1376171 |
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Covering a triangle with sequences of its homothetic copies (English)
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8 December 1999
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It is proved that a triangle or area \(A\) can be covered by translates of any finite collection of -- positive or negative -- homothetic copies, if the total area of the copies is at least \(4A\). This result was conjectured by K. Böröczky; it generalizes a result by \textit{E. Vásarhelyi} [Beitr. Algebra Geom. 17, 61-70 (1984; Zbl 0554.52011)] which admits only negative homothetic copies.
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planar geometry
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covering by homothetic copies
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0.94265735
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0.8892807
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0.8837502
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0.88358855
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