Cake Number
"A cake number is the maximum number of pieces into which a 3dimensional space can be cut with a given number of plane cuts. It is so called because one imagines each such slice cutting a cake. If n planes are available then the number is
The sequence of cake numbers (sequence A000125 in OEIS) for n = 0, 1, 2, 3... is:
1, 2, 4, 8, 15, 26, 42, 64, 93, 130, ....
The first few terms are powers of 2, and an induction argument might wrongly say that each new cut can split each existing part in half, so it is an easy mistake to state that all the terms are powers of 2.
The cake numbers are the 3dimensional analogue of the 2dimensional lazy caterer's sequence; the difference between successive cake numbers also gives the lazy caterer's sequence."
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"What is life? It is the flash of a firefly in
the night. It is the breath of a buffalo
in the wintertime. It is the little shadow
which runs across the grass and loses
itself in the sunset."
