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magic square 3x3 sum 45

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In a magic square 3x3, if we take numbers from 1 to 9  then the magic sum equal to 15. The magic square is as follows:
4
9
2
 3
5
7
8
1
6
In the above magic square 3x3 magic sum is 15. In the above magic square 3x3 we are used numbers from1 to 9, arranged in 9 boxes. In any direction the sum equal to 15.
Row wise  4+9+2=15, 3+5+7=15, 8+1+6=15.
Column wise 4+3+8=15, 9+5+1=15, 2+7+6=15.
Diagnol wise: 4+5+6=15, 2+5+8=15.
The above magic square also can be written as follows:
5-1
5+4
5-3
 5-2
5
5+2
5+3
5-4
5+1
In the above figure , shows the relation between middle number and other numbers. In the magic square we are taken numbers from 1 to 9 and number 5 is between 1 to 9.
If we write  x in place of 5 in above magic square.                                        
X-1
X+4
X-3
 X-2
X
X+2
X+3
X-4
X+1


Now we will write  magic square 3X3 with  magic sum=45
 The magic sum is 45, means the middle number of magic  sqare is 45/3 =15.
then the numbers of magic square are 11,12,13,14,15,16,17,18,19

MAGIC SUM=45. NUMBERS:11,12,13,14,15,16,17,18,19 . MIDDLE NUMBER: 15
       
15-1
15+4
15-3
 15-2
15
15+2
15+3
15-4
15+1
Result of above magic square:
14
19
12
 13
15
17
18
11
16

 This is a magic square 3X3 with the magic sum of 45.

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