Concentric magic square

 

Mathematicians know that a 4x4 concentric magic square consists. In the 2x2 centre you do not find the 4 middele numbers of the 4x4 square, because it is not possible to get a valid magic square. In the border the lowest number is opposite to the highest number, the second lowest number is opposite to the second lowest number, ...

 

Mathematicians know that the 4x4 concentric magic square is a symmetric magic square, for example the famous Dürer magic square.

 

 

16

3

2

13

5

10

11

8

9

6

7

12

4

15

14

1

 

 

Add 10 to all numbers of the 4x4 magic square and construct a 6x6 border with the lowest and the highest numbers. So you get a 4x4 in 6x6 concentric magic square. Add 14 to all numbers of the 4x4 in 6x6 magic square and construct a 8x8 border with the lowest and the highest numbers. So you get a 4x4 in 6x6 in 8x8 concentric magic square. You can put borders around it to infinite.

 

Remove the border of a 4x4 in 6x6 in 8x8 in 10x10 concentric magic square and you get an (impure) 8x8 magic square. Remove the border and you get a 6x6 magic square. Remove the border and you get a 4x4 magic square.

 

 

See how the concentric magic square on this website is growing bigger and bigger: 

3x34x45x56x67x78x89x910x1011x1112x1213x1314x1415x1516x1617x1718x1819x1920x2021x2122x2223x2324x2425x2526x2627x2728x2829x29,  30x3031x31 and 32x32