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arXiv math/0502564math.MG
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三维空间中四个三角形的切线

Line tangents to four triangles in three-dimensional space

Hervé Brönnimann, Olivier Devillers, Sylvain Lazard, Frank Sottile

摘要:

我们研究R^3中与四个三角形相切的直线。在一个构造中,可以有多达62条切线。我们发现,有最多162个连接组件的切线,最多156,如果三角形是不相交的。此外,如果三角形处于(代数)一般位置,则切线的数量是有限的,并且总是偶数。

英文摘要:

We investigate the lines tangent to four triangles in R^3. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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