2007•Journal of Hefei University of TechnologyRequires access
Generalization of inequalities for volumes of pedal simplexes
Yang Shi-guo
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Abstract
Recent studies on the geometric inequality for the n-dimensional simplex produce many important geometric inequalities;however,the study on the problem of the geometric inequality for the pedal simplex has been very few.In this paper,by using the analytic method and the theory of the geometric inequality,the problem of the geometric inequality for the pedal simplex of a simplex in En is discussed,and some inequalities for the volumes of a simplex and its pedal simplex are established.As the special case,some known inequalities for the volumes of the simplex and its pedal simplex are improved.At the same time,a class of inequalities for the vertex angle and the dihedral angle of the n-dimensional simplex are got in the proving of main results.