Multiplicative magic square
A multiplicative magic square is a variant of the general magic square. It is a special number square in which the product of the numbers in each row, each column and each diagonal is always the same.
properties
All the properties that relate to sums in the case of the additive magic squares can be transferred analogously to products.
The conversion from magic sum squares to magic product squares is based on the first power law :
Equal base powers are multiplied by adding their exponents.
Example three square:
The 8 products of the numbers in each row, column and diagonal result in the magic product 32,768 .
Example Duerer's square:
With Albrecht Dürer's magic square , all 86 total combinations of the magic number become 86 product combinations of the magic number in an analogous manner.
The 10 products of the numbers in each row, column and diagonals and the other 76 combinations each result in the magic product 17,179,869,184 .