Magic in mathematics

Author: Kasper B. Graversen, 28/06/08
Keywords: Fun
Abstract: With a bit of addition and multiplication, you can easily create beautiful patterns. Here are some of my favorites to get you started.

Magic in mathematics

“Mathematics may be defined as the subject in which we never know what we are talking about,
nor whether what we are saying is true.”
-- Bertrand Russell
Most people know that 1 * 1 = 1, fewer have realized that 11 * 11 = 121. Nothing too special about that. But hey, try one more: 111 * 111 = 12321. 1-2-3-2-1 hmm.. interesting.. what about 111111111 * 111111111 Yes you gussed it! 12345678987654321. I leave you to fill out the gaps or even continuing adding extra numbers! With a bit of addition and multiplication you can create a lot of fun patterns. Here are my favorites. Can you find more patterns? If you do find anything of interest, email me so I can post it here. 
        1 * 8 + 1 = 9
       12 * 8 + 2 = 98
      123 * 8 + 3 = 987
     1234 * 8 + 4 = 9876
    12345 * 8 + 5 = 98765
   123456 * 8 + 6 = 987654
  1234567 * 8 + 7 = 9876543
 12345678 * 8 + 8 = 98765432
123456789 * 8 + 9 = 987654321
Try using 9 instead of 8... 
        1 * 9 + 2  = 11
       12 * 9 + 3  = 111
      123 * 9 + 4  = 1111
     1234 * 9 + 5  = 11111
    12345 * 9 + 6  = 111111
   123456 * 9 + 7  = 1111111
  1234567 * 9 + 8  = 11111111
 12345678 * 9 + 9  = 111111111
123456789 * 9 + 10 = 1111111111
And its reverse.. 
       9 * 9 + 7 = 88
      98 * 9 + 6 = 888
     987 * 9 + 5 = 8888
    9876 * 9 + 4 = 88888
   98765 * 9 + 3 = 888888
  987654 * 9 + 2 = 8888888
 9876543 * 9 + 1 = 88888888
98765432 * 9 + 0 = 888888888
finally, 
        1 * 1         =         1
       11 * 11        =        121
      111 * 111       =       12321
     1111 * 1111      =      1234321
    11111 * 11111     =     123454321
   111111 * 111111    =    12345654321
  1111111 * 1111111   =   1234567654321
 11111111 * 11111111  =  123456787654321
111111111 * 111111111 = 12345678987654321
Have fun..



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