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.
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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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