Beauty of mathematics

[Abhijeet Digraskar]

Beauty of Mathematics!

                  1 x 8 + 1 = 9
                 12 x 8 + 2 = 98 
                123 x 8 + 3 = 987
               1234 x 8 + 4 = 9876
              12345 x 8 + 5 = 98765 
             123456 x 8 + 6 = 987654
            1234567 x 8 + 7 = 9876543
           12345678 x 8 + 8 = 98765432
          123456789 x 8 + 9 = 987654321 


                  1 x 9 + 2 = 11
                 12 x 9 + 3 = 111 
                123 x 9 + 4 = 1111
               1234 x 9 + 5 = 11111
              12345 x 9 + 6 = 111111
             123456 x 9 + 7 = 1111111 
            1234567 x 9 + 8 = 11111111
           12345678 x 9 + 9 = 111111111
          123456789 x 9 +10 = 1111111111


                  9 x 9 + 7 = 88 
                 98 x 9 + 6 = 888 
                987 x 9 + 5 = 8888
               9876 x 9 + 4 = 88888
              98765 x 9 + 3 = 888888
             987654 x 9 + 2 = 8888888
            9876543 x 9 + 1 = 88888888 
           98765432 x 9 + 0 = 888888888

Brilliant, isn't it?

And finally, take a look at this symmetry:

                   1 x 1 = 1 
                  11 x 11 = 121
                 111 x 111 = 12321
                1111 x 1111 = 1234321
               11111 x 11111 = 123454321
              111111 x 111111 = 12345654321
             1111111 x 1111111 = 1234567654321
            11111111 x 11111111 = 123456787654321 
           111111111 x 111111111 = 12345678987654321


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Regards
Abhijeet Digraskar
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