研究了三角比度量在单位圆盘内的上下界,分别证明了三角比度量与距离比度量、双曲度量、Cassini度量和Gromov双曲度量等四个度量的比较关系.特别地,证明了三角比度量与这些双曲型度量之间不等式的精确性.“,”The purpose of this paper is to establish upper and lower bounds for the triangular ratio metric,and to present geometric properties of the triangular ratio metric by comparing it with the distance ratio metric,the hyperbolic metric,the Cassinian metric,and a Gromov hyperbolic metric.In particular,we show the sharpness of the inequalities between the triangular ratio metric and these hyperbolic type metrics.