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Fair partitions of polygons: An elementary introduction

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Abstract

We introduce the question: Given a positive integer N, can any 2D convex polygonal region be partitioned into N convex pieces such that all pieces have the same area and the same perimeter? The answer to this question is easily ‘yes’ for N = 2. We give an elementary proof that the answer is ‘yes’ for N = 4 and generalize it to higher powers of 2.

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Acknowledgements

Discussions with John Rekesh, Pinaki Majumdar, Arun Sivaramakrishnan and researchers at DAIICT, Gandhinagar were of great help. Thanks to Kingshook Biswas for his guidance and advice.

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Authors and Affiliations

  1. ‘Kovilet’, Palace 41 Compound, Tripunithura, 682 301, India

    R NANDAKUMAR

  2. B-206, Maha Lakshmi Estates, Prashanthi Nagar, Nizampet Road, Hyder Nagar, Hyderabad, 500 085, India

    N RAMANA RAO

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  1. R NANDAKUMAR
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  2. N RAMANA RAO
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Correspondence to R NANDAKUMAR.

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NANDAKUMAR, R., RAMANA RAO, N. Fair partitions of polygons: An elementary introduction. Proc Math Sci 122, 459–467 (2012). https://doi.org/10.1007/s12044-012-0076-5

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  • DOI: https://doi.org/10.1007/s12044-012-0076-5

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