| On the Helly Number for Line Transversals to Parallel Triangles |
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| 引用本文： | 苏战军,丁仁. On the Helly Number for Line Transversals to Parallel Triangles[J]. 东北数学, 2004, 0(1) |
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| 作者姓名： | 苏战军 丁仁 |
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| 作者单位： | Department of Mathematics，Hebei Normal University，Shijiazhuang，050016，Department of Mathematics，Hebei Normal University，Shijiazhuang，050016 |
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| 基金项目： | The NSF (199174) of Hebei Province, China. |
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| 摘 要： | We prove two results about the problem of finding the Helly number for line transversals to a family of parallel triangles in the plane: (1) If each three triangles of a family of parallel right triangles are intersected by an ascending (or a descending) line, then there is an ascending (or a descending) line that intersects all
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On the Helly Number for Line Transversals to Parallel Triangles |
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| SU Zhan-jun and DING Ren. On the Helly Number for Line Transversals to Parallel Triangles[J]. Northeastern Mathematical Journal, 2004, 0(1) |
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| Authors: | SU Zhan-jun and DING Ren |
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| Abstract: | We prove two results about the problem of finding the Helly number for line transversals to a family of parallel triangles in the plane: (1) If each three triangles of a family of parallel right triangles are intersected by an ascending (or a descending) line, then there is an ascending (or a descending) line that intersects all the triangles of the family; (2) If each three triangles of a family of parallel obtuse triangles are intersected by an ascending (or a descending) line, then there is an ascending (or a descending) line that intersects all the triangles of the family. We also obtain that the Helly number of a family of parallel right or obtuse triangles is 3. |
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| Keywords: | Helly number parallel triangle line transversal convex set right tri-angle obtuse triangle acute triangle |
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