到三定点相对距离的和等于定数的点的轨迹
THE LOCUS OF POINTS WITH EQUAL SUM OF RELATIVE DISTANCES TO THREE POINTS

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.
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