本文对国内初等数学书刊上的某些不等式的证明、加强、推广以及上下界估计进行较为深入的讨论,得出了部分有趣的结果. §1 一个几何不等式的上界估计 约定△ABC的边长、半周长、面积、外接圆半径、内切圆半径、旁切圆半径分别为a、b、c,p,△,R,r,r_a、r_b、r_c,且p_a=p—a、p_b=p—b、p_c=p—c,△A′B′C′的上述几何量 In this paper, some inequalities in the domestic elementary mathematics publications are discussed, strengthened, popularized and the upper and lower bounds are discussed in depth. Some interesting results are obtained. §1 The upper bound of a geometrical inequality is the margin of the length of ABC. , semicircumference, area, radius of circumcircle, radius of inscribed circle, and radius of side circle are respectively a, b, c, p, △, R, r, r_a, r_b, r_c, and p_a=p_a, p_b= P-b, p_c=p-c, △A’B’C’ above the amount of geometry