TETRAHEDRA PASSING THROUGH A TRIANGULAR HOLE
TETRAHEDRA PASSING THROUGH A TRIANGULAR HOLE
复制标题
通过三角形孔的四面体
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Bstract
中科院分区：
文献类型：
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作者：
Hiroshi Maehara;N. Tokushige;Bstract
我们证明了一个嵌入定理，即凸体可以穿过三角孔 Δ 当且仅当凸体可以全等地嵌入底边为 Δ 的直角三棱柱中。将其与三棱柱中正四面体全等嵌入的已知结果相结合，我们表明，当且仅当孔的边长大于或等于 (1 + √ 2)/ √ 6 ≈ 0.9856 时，具有单位边的正四面体才能穿过平面中的等边三角形孔。为了证明嵌入定理，我们使用三角形框架不能容纳凸体的事实。另一方面，我们还证明每个非三角形框架可以容纳一些四面体，并且每个n边形框架（n≥4）可以固定一些四面体。
We prove an embedding theorem that says a convex body can pass through a triangular hole ∆ if and only if the convex body can be congruently embedded in a right triangular prism with base ∆. Combining this with a known result on congruent embeddings of a regular tetrahedron in a triangular prism, we show that a regular tetrahedron with unit edge can pass through an equilateral triangular hole in a plane if and only if the edge length of the hole is greater than or equal to (1 + √ 2)/ √ 6 ≈ 0.9856. For the proof of the embedding theorem we use the fact that no triangular frame can hold a convex body. On the other hand, we also show that every non-triangular frame can hold some tetrahedron, and every n-gon frame (n ≥ 4) can fix some tetrahedron.
DOI：
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发表时间：
2006
期刊：
Rendiconti del Circolo Matematico di Palermo 77
影响因子：
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作者：
J.Itoh;Y.Tanoue and;T.Zamfirescu
通讯作者：
T.Zamfirescu