The average number of regions into which
(Finch 2003, p. 482).
The maximum number of regions is presumably the same as for space
division by planes , namely
(Yaglom and Yaglom 1987, pp. 102-106). For A000125 ), a sequence whose values
are sometimes called the "cake numbers "
due to their relation to the cake cutting problem.
See also Cake Number ,
Cake Cutting ,
Cylinder Cutting ,
Space
Division by Planes ,
Square Division by
Lines
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References Finch, S. R. Mathematical Constants. Sloane,
N. J. A. Sequence A000125 /M1100
in "The On-Line Encyclopedia of Integer Sequences." Yaglom,
A. M. and Yaglom, I. M. Challenging
Mathematical Problems with Elementary Solutions, Vol. 1. Referenced on Wolfram|Alpha Cube Division by Planes
Cite this as:
Weisstein, Eric W. "Cube Division by Planes."
From MathWorld https://mathworld.wolfram.com/CubeDivisionbyPlanes.html
Subject classifications
randomly chosen planes divide a cube is
, 2, ... planes, this gives the values 2, 4, 8, 15, 26, 42,
... (OEIS A000125), a sequence whose values
are sometimes called the "cake numbers"
due to their relation to the cake cutting problem.
