Abstract：In this paper, We discuss problem of geometric inequalities for vertex distance and face areas and volumes of two simplexes in the Euclidean space E''. By using the power mean inequality, inequality of arithmetic and geometric mean , the Chebyshev inequality and $τ_{n}=[1+\frac{(M-m)^{2}}{(n+1)M^{2}}]^{\frac{n+1}{2n}}\ge 1,τ'_{n}=[1+\frac{(M'-m')^{2}}{(n+1)M^{'2}}]^{\frac{n+1}{2n}}\ge 1$, we obtain some geometric inequalities for vertex distance and face areas and volumes of two simplexes. These inequalities are the generalizations of the known results.
陈士龙. 关于两个单形顶点的距离、侧面积及体积的不等式及其应用[J]. 浙江大学学报（理学版）, 2020, 47(1): 81-85.
CHEN Shilong. Inequlities for vertex distances and face areas and volumes of two simplexes with applications. Journal of ZheJIang University(Science Edition), 2020, 47(1): 81-85.
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2020, Vol. 47 
