某些凸的光滑闭图形的特殊性质

A Special Property of Some Convex and Smooth Closed Graphs

在R2中,通过定义凸的光滑闭图形G的特征直径A为G的外接圆的直径,G的标准化周长D为图形G的周长与其特征直径A的比值。得到了某些凸的光滑(或分段光滑)闭图形的一个共同性质:G的标准化周长D∈[2,π]。

In R2,by defining the characteristic diameter A of convex and smooth closed graph G as the diameter of G＇s circumcircle and defining G＇s standardized perimeter D as the ratio of G＇s perimeter to its characteristic diameter A,a common property of some convex and smooth closed graphs will be obtained： G＇s standardized perimeter D is in .