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Slicing the Cube
Zach, David

2011, BS, Kent State University, College of Arts and Sciences / Department of Mathematical Science.
In this paper, we investigate extremal volumes of slices of the n-dimensional unit cube. If a cube is sliced by a central hyperplane, the maximal and minimal volumes of intersection are known, but the arguments are much more complex than one would expect to see for such a straightforward, geometrical query. Furthermore, if we dictate that the hyperplane must be a certain distance t from the center of the cube, then very little is known about the optimal volumes of intersection. This paper presents a brief history of this problem, and then gives a full solution for extremal one-dimensional slices and a partial solution for extremal hyperplane slices, when t is greater than ½√(n-1).
Artem Zvavitch, Ph.D. (Advisor)
Feodor Dragan, Ph.D. (Committee Member)
Brett Ellman, Ph.D. (Committee Member)
Jenya Soprunova, Ph.D. (Committee Member)
29 p.

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Zach, D. (2011). Slicing the Cube. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Zach, David. "Slicing the Cube." Electronic Thesis or Dissertation. Kent State University, 2011. OhioLINK Electronic Theses and Dissertations Center. 30 Jun 2015.

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Zach, David "Slicing the Cube." Electronic Thesis or Dissertation. Kent State University, 2011. https://etd.ohiolink.edu/

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