Mathematical magic squares

Mathematical magic squares

The Mathematical magic squares can be easily made with any sequence of the arithmetic progression like numbers forms squares.

e.g the numbers 1 to 9 can be arranged as square which gives the sum of any row or column or cross line gives same.

i.e the total numbers[n]=9

The sum n number of natural numbers=n[n+1]

                                                                     2

                                                            =9[9+1]

                                                                   2

                                                             =9x10

                                                                  2

                                                            =9x5=45

The sum of the each row/column/ cross line=45/3=15

Please observe the process as below

 Finally check the each row or column or cross line total

Rows

         4+9+2=15

         3+5+7=15

         8+1+6=15

Columns

         4+3+8=15

         9+5+1=15

         2+7+6=15

Cross lines

         4+5+6=15

         2+5+8=15

The magic squares gives fun and creates interest on mathematics to children and improve the knowledge about numbers.

As above any arithmetic progression numbers can written as magic squares

e.g: arithmetic progression: 1, 3, 5, 7,…………17

Sum of the ‘n’numbers [i.e sum of odd numbers]=n²=9²=81

The sum of the each row or column or cross line=81/3=27

Check the sum of each line i.e row or column or cross line

Sum of 1^st row numbers=7+17+3=27
      Sum of 2^nd row numbers=5+9+13=27

            Sum of 3^rd row numbers=15+1+11=27

             Sum of 1^st column numbers=7+5+15=27

     Sum of 2^nd column numbers=17+9+1=27

Sum of 3^rd column numbers=3+13+11=27

Sum of 1^st cross line numbers=7+9+11=27

          Sum of 2nd cross line numbers=3+9+15=27