Minimum Area Isosceles Containers
| Autor: | Gergely Kiss, János Pach, Gábor Somlai |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Information Processing. 28:759-765 |
| ISSN: | 1882-6652 |
| DOI: | 10.2197/ipsjjip.28.759 |
| Popis: | We show that every minimum area isosceles triangle containing a given triangle $T$ shares a side and an angle with $T$. This proves a conjecture of Nandakumar motivated by a computational problem. We use our result to deduce that for every triangle $T$, (1) there are at most $3$ minimum area isosceles triangles that contain $T$, and (2) there exists an isosceles triangle containing $T$ whose area is smaller than $\sqrt2$ times the area of $T$. Both bounds are best possible. |
| Databáze: | OpenAIRE |
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