Magic tesseract
In
mathematics, a
magic tesseract is the 4-dimensional generalization of a
magic square and
magic cube, that is, a number of
integers arranged in an
n x
n x
n x
n pattern such that the sum of the numbers on each pillar (along any axis) as well as the main space diagonals is equal to a single number, the so-called magic constant of the
tesseract, denoted
M4(
n). It can be shown that if a magic tesseract consists of the numbers 1, 2, ...,
n4, then it has magic number (
Sloane's
A021003)
If, in addition, the numbers on every
cross section diagonal also sum up to the tesseract's magic number, the tesseract is called a
perfect magic tesseract; otherwise, it is called a
semiperfect magic tesseract. The number
n is called the order of the magic tesseract.
See also