四面体的Bonnesen型等周不等式  

On the Bonnesen-type Isoperimetric Inequality for the Tetrahedron

作　　者：彭璐 马磊 曾春娜 PENG Lu;MA Lei;ZENG Chunna(College of Mathematics Science,Chongqing Normal University,Chongqing 401331,China;Department of Education,Maoming Infant Teachers College,Maoming 525000,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]广东茂名幼儿师范专科学校教育系,广东茂名525000

出　　处：《湖北民族学院学报（自然科学版）》2019年第3期287-290,共4页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(11801048);重庆市留学人员创新创业支持计划(cx2018034);重庆市科学技术委员会重庆市前沿与应用基础研究项目(cstc2017jcyjAXOO22)

摘　　要：主要通过研究平面上四面体的表面积、体积和内切球半径之间的关系,并借助一系列几何不等式、均值不等式等,获得了四面体的几个新的Bonnesen型不等式.进一步还给出了四面体的等周不等式的新的证明方法.最后猜想获得用ri与re表示新的四面体的Bonnesen型不等式.By applying the relations of the surface area,volume and radius of inscribed sphere,and following a series of geometric inequalities and the average value inequalities,we obtain some new Bonnesen-type inequalities of tetrahedral.Furthermore we also give a new proof of isoperimetric inequality of tetrahedron.Lastly we guess by this method to obtain some new Bonnesen-type inequalities on tetrahedral of the expressions of r i and r e.

关 键 词：四面体 体积 表面积 内切球半径 Bonnesen型等周不等式 

分 类 号：O186.5[理学—数学]