Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (6): 1162-1168.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 52A10
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