Equal Area Polygons in Convex Bodies

  • T. Sakai
  • C. Nara
  • J. Urrutia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)


In this paper, we consider the problem of packing two or more equal area polygons with disjoint interiors into a convex body K in E 2 such that each of them has at most a given number of sides. We show that for a convex quadrilateral K of area 1, there exist n internally disjoint triangles of equal area such that the sum of their areas is at least \(\frac {4n} {4n+1}\). We also prove results for other types of convex polygons K. Furthermore we show that in any centrally symmetric convex body K of area 1, we can place two internally disjoint n-gons of equal area such that the sum of their areas is at least \(\frac {n-1}{\pi} sin \frac {\pi}{n-1}\). We conjecture that this result is true for any convex bodies.


Intersection Point Convex Body Convex Polygon Circular Disk Equal Area 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • T. Sakai
    • 1
  • C. Nara
    • 1
  • J. Urrutia
    • 2
  1. 1.Research Institute of Educational DevelopmentTokai UniversityShibuya-ku, TokyoJapan
  2. 2.Instituto de Matemáticas, Ciudad UniversitariaUniversidad Nacional Autónoma de MéxicoMéxico D.F.México

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