n维Euler不等式的改进

Improvement of n-dimensional euler inequality

应用距离几何理论和解析方法研究了n维欧氏空间En中n维单形的外接球半径与内切球半径之间的不等式关系,以及单形体积与棱长之间的不等式关系.将欧氏平面上三角形的Finsler-Hadwiger不等式推广到n维单形,给出了n维Euler不等式的一个改进.

The theory of distance geometry and the analytic method is used to study the inequality for circumradius and inradius and for the volume and edge-lengths of an n-dimensional simplex in the n-dimensional Euclidean space E^n. The Finsler-Hadwiger inequality for a triangle in the Euclidean plane is extended to an n-dimensional simplex, and n-dimensional Euler inequality is improved.