| 到三定点相对距离的和等于定数的点的轨迹 |
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| 引用本文： | 李晓玲,张素梅,张更生,沈建.到三定点相对距离的和等于定数的点的轨迹[J].数学杂志,2016,36(4):759-766. |
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| 作者姓名： | 李晓玲 张素梅 张更生 沈建 |
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| 作者单位： | 河北师范大学数学与信息科学学院, 河北 石家庄 050024,邯郸学院数理学院, 河北 邯郸 056005,河北师范大学数学与信息科学学院, 河北 石家庄 050024 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11371121); Na- tional Natural Science Foundation of USA (CNS 0835834; DMS 1005206); Natural Science Foundation of Hebei Province (A2013205073); Science Foundation of Hebei Normal University (L2013Z01). |
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| 摘 要： | 本文研究了相对测度空间中的距离问题. 利用质点几何的理论方法获得如下结果:对任意给定的实数, 满足条件dT (P,A) + dT (P,B) + dT (P,C) =τ的点P的轨迹是凸十二边形或九边形(其中T:=ABC 是由给定的不同三点A, B, C构成的三角形), 所得结果丰富了相对距离研究领域的内容.
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| 关 键 词： | 相对距离 平面凸体 十二边形 |
| 收稿时间： | 2014/4/9 0:00:00 |
| 修稿时间： | 2014/6/11 0:00:00 |
THE LOCUS OF POINTS WITH EQUAL SUM OF RELATIVE DISTANCES TO THREE POINTS |
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| LI Xiao-ling,ZHANG Su-mei,ZHANG Geng-sheng and SHEN Jian.THE LOCUS OF POINTS WITH EQUAL SUM OF RELATIVE DISTANCES TO THREE POINTS[J].Journal of Mathematics,2016,36(4):759-766. |
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| Authors: | LI Xiao-ling ZHANG Su-mei ZHANG Geng-sheng and SHEN Jian |
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| Institution: | School of Mathematics and Information Sciences, Hebei Normal University, Shijiazhuang 050024, China,School of Mathematics and Physics, Handan College, Handan 056005, China,School of Mathematics and Information Sciences, Hebei Normal University, Shijiazhuang 050024, China and Department of Mathematics, Texas State University, San Marcos TX78666, USA |
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| Abstract: | In this paper, we study the problem about relative distance in the relative metric space. By mass point geometry, we get the result that for any given real number τ > 4, the locus of the points P satisfying the condition, dT (P,A)+dT (P,B)+dT (P,C) = τ, is a convex dodecagon or nonagon (where T ≡ ABC is a triangle formed by the three fixed points A, B, and C), which enriches the field of relative distance. |
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| Keywords: | relative distance plane convex body dodecagon |
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