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The original problem that serves as a basis for this project comes from an American contest (PUMaC, 2014) regarding the maximum amount of enclosed spaces given a limited number of cuts on an infinite plane. In this study, we explore the same problem and extend it in the context of m dimensions given n (m-1) dimensional cuts using the recursive relationship of finite cuts and enclosed spaces in lower dimensions. Once the general formula of f(m,n)?was proven for dimensions, an Euler¡¯s inspired formula was used to check the accuracy of the formula in two and three dimensions. The Euler¡¯s formula also allowed us to derive the formula for the maximum number of unenclosed spaces in three-dimensional F(3, n). The results are as follows:

Author

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  • Erick C. Huang
  • Sharon S. Huang
  • Cheng-Hua Tsai

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Suggested Citation

  • Erick C. Huang & Sharon S. Huang & Cheng-Hua Tsai, 2017. "The original problem that serves as a basis for this project comes from an American contest (PUMaC, 2014) regarding the maximum amount of enclosed spaces given a limited number of cuts on an infinite ," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 49-68, August.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:49-68
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    Keywords

    finite field; recursive relations; Euler characteristic;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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