JIPAM logo: Home Link
 
Home Editors Submissions Reviews Volumes RGMIA About Us
 

   
  Volume 10, Issue 3, Article 74
 
On the Interpoint Distance Sum Inequality
    Authors: Yong Xia, Hong-Ying Liu,  
    Keywords: Combinatorial geometry, Distance geometry, Interpoint distance sum inequality, Optimization.  
    Date Received: 10/04/2009  
    Date Accepted: 28/09/2009  
    Subject Codes:

51D20, 51K05, 52C26.

  
    Editors: Peter S. Bullen,  
 
    Abstract:

Let $ n$ points be arbitrarily placed in $ B(D)$, a disk in $ mathbb{R}^2$ having diameter $ D$. Denote by $ l_{ij}$ the Euclidean distance between point $ i$ and $ j$. In this paper, we show

$displaystyle sum_{i=1}^n left(min_{j<br />eq i}l_{ij}^2ight) leq frac{D^2}{0.3972}.$    
We then extend the result to $ mathbb{R}^3$.

         
       
  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page
  

      search [advanced search] copyright 2003 terms and conditions login