Amazing Number Pyramids

The following equalities are obvious, but they are beautiful nonetheless.

        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


       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


              12 - 1 = 11
            123 - 12 = 111
          1234 - 123 = 1111
        12345 - 1234 = 11111
      123456 - 12345 = 111111
    1234567 - 123456 = 1111111
  12345678 - 1234567 = 11111111
123456789 - 12345678 = 111111111

I hope you enjoyed these beautiful equations. Another type of beautiful formulas are continuous fractions and infinite sum series that I hope to post about them later.

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