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

Erick C. Huang, Sharon S. Huang and Cheng-Hua Tsai

Journal of Mathematics Research, 2017, vol. 9, issue 4, 49-68

Keywords: finite field; recursive relations; Euler characteristic (search for similar items in EconPapers)
Date: 2017
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