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Update of Oct. 19, 2003:
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Lies De SutterThese squares are complete- and self-similar
square and have special constellation patterns all at a time!
(1) complete property;
In the squares, not only the major but also the minor diagonals
add up to the same number, 65.
For example:
A * * * * * B * * * * * C * * * * * D * A + B + C + D + E = 65 (Major diagonal) * * * * E * A * * * * * B * * * * * C * * * * * D A + B + C + D + E = 65 E * * * * * * A * * * * * B * * * * * C D * * * * A + B + C + D + E = 65 * E * * * ... ... and so on.
(2) Self complement;
The square is invariant for the complemental transform. If you
change all the number "n" of the square by
"26-n" , you get the rotated same square.
You can say that it is axisymmetry or self-simillar, in another
word.
(3) five-star constellation patterns;
Sum of the five numbers of all small squares and the centers sum
to the same number, 65.
1 * * * 9 1 * 22 * * * 15 * 18 * * * 22 * 9
* * * * * * 19 * * * * * 6 * * * * * 5 *
* * 13 * * 10 * 13 * * * 2 * 24 * * * 13 * 16
* * * * * * * * * * * * * * * * * * * *
17 * * * 25 * * * * * * * * * * * * * * *
....
....
* * * * *
* * * * *
* * 13 * 16
.... .... .... .... .... * * * 7 *
* * 4 * 25
Rhonbohedral patterns;
Furthermore, five numbers of all small rhonbohedrons add up to
the same number, 65.
* 15 * * * * * 22 * *
23 19 6 * * * 19 6 5 *
* 2 * * * * * 13 * *
* * * * * * * * * *
* * * * * * * * * * ......
......
......
* * * * * * * 22 * *
* * * * * * * * * *
* * * 24 * 10 * 13 * 16
* * 20 7 3 * * * * *
* * * 11 * * * 4 * *
| ( 1) 1 15 22 18 9 23 19 6 5 12 10 2 13 24 16 14 21 20 7 3 17 8 4 11 25 |
( 2) 1 15 24 18 7 23 17 6 5 14 10 4 13 22 16 12 21 20 9 3 19 8 2 11 25 |
( 3) 1 23 20 12 9 15 7 4 21 18 24 16 13 10 2 8 5 22 19 11 17 14 6 3 25 |
( 4) 1 23 20 14 7 15 9 2 21 18 22 16 13 10 4 8 5 24 17 11 19 12 6 3 25 |
| ( 5) 2 14 21 18 10 23 20 7 4 11 9 1 13 25 17 15 22 19 6 3 16 8 5 12 24 |
( 6) 2 14 25 18 6 23 16 7 4 15 9 5 13 21 17 11 22 19 10 3 20 8 1 12 24 |
( 7) 2 23 19 11 10 14 6 5 22 18 25 17 13 9 1 8 4 21 20 12 16 15 7 3 24 |
( 8) 2 23 19 15 6 14 10 1 22 18 21 17 13 9 5 8 4 25 16 12 20 11 7 3 24 |
| ( 9) 4 12 21 18 10 23 20 9 2 11 7 1 13 25 19 15 24 17 6 3 16 8 5 14 22 |
(10) 4 12 25 18 6 23 16 9 2 15 7 5 13 21 19 11 24 17 10 3 20 8 1 14 22 |
(11) 4 23 17 11 10 12 6 5 24 18 25 19 13 7 1 8 2 21 20 14 16 15 9 3 22 |
(12) 4 23 17 15 6 12 10 1 24 18 21 19 13 7 5 8 2 25 16 14 20 11 9 3 22 |
| (13) 5 11 22 18 9 23 19 10 1 12 6 2 13 24 20 14 25 16 7 3 17 8 4 15 21 |
(14) 5 11 24 18 7 23 17 10 1 14 6 4 13 22 20 12 25 16 9 3 19 8 2 15 21 |
(15) 5 23 16 12 9 11 7 4 25 18 24 20 13 6 2 8 1 22 19 15 17 14 10 3 21 |
(16) 5 23 16 14 7 11 9 2 25 18 22 20 13 6 4 8 1 24 17 15 19 12 10 3 21 |
Note :
We found most of the information on Magic Squares on the Internet.