| 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. |
| 关键词: 相对距离 平面凸体 十二边形 |
| DOI： |
| 分类号:O157.3 |
| 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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| THE LOCUS OF POINTS WITH EQUAL SUM OF RELATIVE DISTANCES TO THREE POINTS |
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LI Xiao-ling1, ZHANG Su-mei2, ZHANG Geng-sheng1, SHEN Jian3
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1.School of Mathematics and Information Sciences, Hebei Normal University, Shijiazhuang 050024, China;2.School of Mathematics and Physics, Handan College, Handan 056005, China;3.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. |
| Key words: relative distance plane convex body dodecagon |
