Pan, Juanjuan; Yang, Shiguo Geometric inequalities and their applications for inscribed simplex. (Chinese. English summary) Zbl 1265.51013 Math. Pract. Theory 41, No. 15, 198-203 (2011). Summary: By using analytic methods, we study the problem of geometric inequalities concerning the \(n\)-dimensional simplex \(\Omega_n\) and its inscribed simplex \(\Omega'_n\) in \(E^n\). Some geometric inequalities for the circumradius of \(\Omega_n\) and \(\Omega'_n\) and their altitude are established. As special case, some generalizations of the famous \(n\)-dimensional Euler inequality are obtained. MSC: 51M16 Inequalities and extremum problems in real or complex geometry 51M20 Polyhedra and polytopes; regular figures, division of spaces 51M25 Length, area and volume in real or complex geometry Keywords:simplex; circumradius; altitude; interior point; inequality PDFBibTeX XMLCite \textit{J. Pan} and \textit{S. Yang}, Math. Pract. Theory 41, No. 15, 198--203 (2011; Zbl 1265.51013)