| 平面Bonnesen等周不等式的进一步加强 |
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| 引用本文： | 吴莉,杨仕椿.平面Bonnesen等周不等式的进一步加强[J].洛阳师范学院学报,2008,27(2):35-36. |
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| 作者姓名： | 吴莉 杨仕椿 |
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| 作者单位： | 阿坝师范高等专科学校数学系,四川汶川,623000 |
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| 基金项目： | 四川省教育厅资助项目，阿坝师专校级科研基金 |
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| 摘 要： | 设欧氏平面R2中域D的面积为A,周长为L,r及R分别为D的最大内接圆半径及最小外接圆半径。利用参考文献中和分几何方法,给出了平面Bonnesen等周不等式的进一步加强,证明了L2-4πA≥π2(R-r)2(πR+πr-L)2.
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| 关 键 词： | Bonnesen等周不等式 积分几何方法 运动公式 域 Euler-Poincare示性数。 |
The further reinforcement of plane Bonnesen's isoperimetric inequalities |
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| WU Li,YANG Shi-chun.The further reinforcement of plane Bonnesen's isoperimetric inequalities[J].Journal of Luoyang Teachers College,2008,27(2):35-36. |
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| Authors: | WU Li YANG Shi-chun |
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| Institution: | Department of Mathematics;Aba Teachers College;Sichuan Wenchuan;623000 |
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| Abstract: | Let D be a domain in the Euclidean R^2. Let A be the area of the domain D, L the perimeter of D, r and R the radiuses smallest circumscribed circle and the biggest inscribed circle of D. In this paper, we give further reinforcement of the plane Bonnesen＇ s isoperimetric inequality by the method of integral geometry. Weproved inequalities ad following L2 - 4πA ≥ π2 （ R - r）^ 2 ＋ （ πR ＋ πr - L） ^2. |
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| Keywords: | plane Bonnesen's isoperimetric inequalities the method of integral geometry kinematic formula domain Euler-Poincare characteristic |
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