In this paper,by using the theory and method of distance geometry,we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length ...In this paper,by using the theory and method of distance geometry,we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space.They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space.展开更多
Yang Lu and Zhang Jingzhong have extended the Neuberg-Pedoe Inequality to the higher space and have given an inequality concerning two simplices (Acta Mathematica Sinica, 24(1981), 401—408). In this note other two in...Yang Lu and Zhang Jingzhong have extended the Neuberg-Pedoe Inequality to the higher space and have given an inequality concerning two simplices (Acta Mathematica Sinica, 24(1981), 401—408). In this note other two inequalities concerning two simplices are presented.展开更多
文摘In this paper,by using the theory and method of distance geometry,we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space.They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space.
文摘Yang Lu and Zhang Jingzhong have extended the Neuberg-Pedoe Inequality to the higher space and have given an inequality concerning two simplices (Acta Mathematica Sinica, 24(1981), 401—408). In this note other two inequalities concerning two simplices are presented.
