The maximal number of regions into which three-dimensional space can be divided by planes is
(Yaglom and Yaglom 1987, pp. 102-106). For , 2, ..., these give 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.
This is the same solution as for cylinder cutting.
The maximum is attained when every two planes intersect in a line, every three intersect in exactly one point,
and no four have a common point.
planes is
, 2, ..., these give 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.
This is the same solution as for cylinder cutting.
