图1、图2是人们熟知的两个图形,它们显示了两个正实数a和b的算术平均(AM)、几何平均(GM)和调和平均(HM)之间的关系.巴布斯在公元320年就在一个半圆图形中作出了这三个均值。本文将引入一个更简单而有趣的图形,它不仅包含了这三个平均,而且包含了平均的一个完整的连续统。算术平均≥几何平均≥调和平均(AM≥GM≥HM)这一熟知的顺序关系,也在包含其它平均的类似顺序关系中一起显示出来。 Figures 1 and 2 are two well-known graphs that show the relationship between the arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM) of two positive real numbers a and b. The three averages were made in a semicircle in AD 320. This article will introduce a simpler and more interesting graph that includes not only the three averages but also a complete continuum of the average. The well-known sequential relationship of arithmetic mean ≥ geometric mean ≥ harmonic mean (AM ≥ GM ≥ HM) is also shown together in similar order relationships that contain other means.