数学物理学报 ›› 2013, Vol. 33 ›› Issue (6): 1162-1168.

• 论文 • 上一篇    下一篇

关于平面常宽凸集等周亏格的注记

张洪1,2|徐文学2*|李泽清2,3   

  1. 1.贵州凯里学院数学科学学院 贵州 凯里 |556011;
    2.西南大学数学与统计学院 重庆 |400715;
    3.贵州毕节学院数学与计算机科学学院 贵州 毕节 |551700
  • 收稿日期:2012-04-17 修回日期:2013-03-06 出版日期:2013-12-25 发布日期:2013-12-25
  • 通讯作者: 徐文学,xwxjk@163.com E-mail:hzhang6619@163.com; xwxjk@163.com; lizeqing63@163.com
  • 基金资助:

    西南大学访学基金和凯里学院基础数学重点学科建设项目基金(KZD2009001)资助

Remarks on the Isoperimetric Deficit of the Planar Isosceles Trapezoids of Constant Width

 ZHANG Hong1,2, XU Wen-Xue2*, LI Ze-Qing2,3   

  1. 1.School of Mathematical Sciences, Kaili University, Guizhou Kaili |556011;
    2.School of Mathematics and Statistics, Southwest University, Chongqing 400715;
    3.School of Mathematics and Computer Science, Bijie University, Guizhou Bijie 551700
  • Received:2012-04-17 Revised:2013-03-06 Online:2013-12-25 Published:2013-12-25
  • Contact: XU Wen-Xue,xwxjk@163.com E-mail:hzhang6619@163.com; xwxjk@163.com; lizeqing63@163.com
  • Supported by:

    西南大学访学基金和凯里学院基础数学重点学科建设项目基金(KZD2009001)资助

摘要:

研究了平面常宽凸集K 的等周亏格, 验证了平面常宽等腰梯形K 的Blaschke-Lebesgue 定理, 即当K 为Reuleaux 三角形时等周亏格最大.

关键词: 等周不等式, 等周亏格, 常宽凸集, 常宽等腰梯形

Abstract:

In this paper, we investigate the isoperimetric deficit of isosceles trapezoid of constant width.  We confirm the known  Blaschke-Lebesgue theorem for isosceles trapezoids of constant width. That is, the isoperimetric deficit of isosceles trapezoids of constant width attains the maximum for the Reuleaux triangle.

Key words: Isoperimetric , inequality, Convex set of constant width;
Isosceles trapezoid of constant width,
Isoperimetric deficit

中图分类号: 

  • 52A10