Geodesic
On a covering problem for equilateral triangles
The electronic journal of combinatorics, Tome 15 (2008)
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Let $T$ be a unit equilateral triangle, and $T_1,\dots,T_n$ be $n$ equilateral triangles that cover $T$ and satisfy the following two conditions: (i) $T_i$ has side length $t_i$ ($0 < t_i < 1$); (ii) $T_i$ is placed with each side parallel to a side of $T$. We prove a conjecture of Zhang and Fan asserting that any covering that meets the above two conditions (i) and (ii) satisfies $\sum_{i=1}^n t_i \geq 2$. We also show that this bound cannot be improved.
DOI : 10.37236/761
Classification : 52C15 
@article{10_37236_761,
     author = {Adrian Dumitrescu and Minghui Jiang},
     title = {On a covering problem for equilateral triangles},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/761},
     zbl = {1160.52014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/761/}
}
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Adrian Dumitrescu; Minghui Jiang. On a covering problem for equilateral triangles. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/761

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