Abstract
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.
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Sakai, T., Nara, C., Urrutia, J. (2005). Equal Area Polygons in Convex Bodies. In: Akiyama, J., Baskoro, E.T., Kano, M. (eds) Combinatorial Geometry and Graph Theory. IJCCGGT 2003. Lecture Notes in Computer Science, vol 3330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30540-8_17
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DOI: https://doi.org/10.1007/978-3-540-30540-8_17
Publisher Name: Springer, Berlin, Heidelberg
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