论文标题
最佳的嵌入式和封闭的同步三角形
Optimal embedded and enclosing isosceles triangles
论文作者
论文摘要
考虑到三角形$δ$，我们研究了确定最小封闭和最大的嵌入等质等质三角形的$δ$相对于面积和周长。这个问题最初是由Nandakumar提出的，首先是由Kiss，Pach和Somlai研究的，他们表明，如果$δ'$是最小的等同基质剂三角形，其中包含$δ$，然后是$Δ'$，$δ$和$Δ$共享一侧和角度。 在本文中，我们证明，对于任何三角形$δ$，每个最大面积等同步三角形嵌入$δ$，每个最大最大的同学三角形三角形嵌入了$δ$ sharees and侧面和$δ$的角度。令人惊讶的是，最小外围封闭三角形的情况是不同的：有一个无限的三角形$Δ$的家族，其最小的边缘同步等同步容器不共享一个侧面和$Δ$的角度。
Given a triangle $Δ$, we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of $Δ$ with respect to area and perimeter. This problem was initially posed by Nandakumar and was first studied by Kiss, Pach, and Somlai, who showed that if $Δ'$ is the smallest area isosceles triangle containing $Δ$, then $Δ'$ and $Δ$ share a side and an angle. In the present paper, we prove that for any triangle $Δ$, every maximum area isosceles triangle embedded in $Δ$ and every maximum perimeter isosceles triangle embedded in $Δ$ shares a side and an angle with $Δ$. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles $Δ$ whose minimum perimeter isosceles containers do not share a side and an angle with $Δ$.
