In mathematics, the cake number, denoted by Cn, is the maximum number of regions into which a 3-dimensional cube can be partitioned by exactly n planes. The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube-shaped cake.
The values of Cn for increasing n ≥ 0 are given by 1, 2, 4, 8, 15, 26, 42, 64, 93, …
The cake numbers are the 3-dimensional analogue of the 2-dimensional lazy caterer's sequence; the difference between successive cake numbers also gives the lazy caterer's sequence.
Read more about Cake Number: General Formula
Famous quotes containing the words cake and/or number:
“The first year was like icing.
Then the cake started to show through.”
—John Ashbery (b. 1927)
“It is always possible to bind together a considerable number of people in love, so long as there are other people left over to receive the manifestations of their aggression.”
—Sigmund Freud (1856–1939)