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Certain Inequalities Concerning Some Kinds Of Chordal Polygons  
 
  Authors: Mirko Radic,  
  Keywords: Inequality, $k$-chordal polygon, $k$-inscribed chordal polygon, index of $k$-inscribed chordal polygon, characteristic of $k$-chordal polygon.  
  Date Received: 09/07/03  
  Date Accepted: 25/11/03  
  Subject Codes:

51E12

  
  Editors: Jozsef Sandor,  
 
  Abstract:

This paper deals with certain inequalities concerning some kinds of chordal polygons (Definition 1.2). The main part of the article concerns the inequality

$\displaystyle \sum_{j=1}^n \cos \beta_j > 2k,$    
where
$\displaystyle \sum_{j=1}^n \beta_j = (n-2k)\frac{\pi}{2}, \quad n-2k>0, \qquad 0<\beta_j< \frac{\pi}{2}, \quad j=\overline{1,n}.$    
This inequality is considered and proved in [5, pp. 143-145]. Here we have obtained some new results. Among others we found some chordal polygons with the property that $ \sum_{j=1}^n \cos^2 \beta_j = 2k$, where $ % n=4k$ (Theorem 2.17). Also it could be mentioned that Theorem 2.19 is a modest generalization of the Pythagorean theorem.;


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