E^n空间二面角的另一类不等式

THE ANOTHER CLASS OF INEQUALITY ABOUT E^n SPATIAL DIHEDRAL ANGLE

在［２］中尹景尧得出关于单纯形的一类三角不等式。本文把不等式：Ａ、Ｂ、Ｃ为ΔＡＢＣ的三内角，推广到ｎ维单形上去并且得另一类关于二面角的不等式．假定Ｅ中非退化单形Δｎ的顶点集Ｓ＝｛Ｐ１，Ｐ２，…，Ｐｎ＋１｝，表示顶点Ｐｉ所对的ｎ－１维侧面，表示侧面Ｆｉ与Ｆｉ所夹的内二面角，即则有下面结论：m为任何自然数；等号当Δｎ为正则单形时取得．

In [2], YIN Jing-rao gets the triangle inequality about simplex. This paper spreads the inequality , here A. B. C stand for the three interior angle of triangle ABC' to n-dimensional simplex field and gets another class of inequality about dihedral angle: here,, is interior dihedral angle of leteral face F, and F,, m, n is arbitrary natural number. The equality is obtained when An is regular simplex.