“'Magic Squares and Linear Algebra' by Christopher J. Henrich in the American Mathematical Monthly, Vol 98, no 6, 1991 has a very interesting 16x16 magic square created by Benjamin Franklin.
Although the diagonals of this square do not sum to 2056, there are many other magical properties. Henrich quotes Franklin as having said, “[it] is the most magically magical of any magic square ever made by any magician.”
All the rows and columns sum to the number 2056, but that is not all. Half rows and half columns sum to 1028.
The sixteen entries in every 4x4 subsquare sum to 2056.
But there is even more!
In the figures above, the bent diagonals going from top to bottom (Figure 1) sum to 2056. Even the broken ones that have two pieces! Follow the colored patterns and you will be able to check this. The other three figures show the other diagonals going from from right to left (Figure 2), from bottom to top (Figure 3) and from left to right (Figure 4) also have sums of 2056.
This magic square was constructed over 200 years ago. Even with the aid of a computer this would be a prodigious task.
Source: math.wichita.edu"
No comments:
Post a Comment