Four Beautiful Christmas Trees

by Lorne Mitchell on 18/12/2011

In celebration of the time of the year, I found these four sets of elegant Mathematical Formulae which I thought would make excellent Christmas Trees!  As we leave 2011, here are two that celebrate the symmetry of eleven:

                               +

                      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

                       =====

                          ===

And here is another that balances the tree above with another set of elevens:

                                   *

                             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

                                =====

                                   ===

And for those of you who believe, like the Chinese, that “8” is lucky, I have dressed this one in red:

                               +

                      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

                           =====

                              ===

And finally this one, my favourite, which took me ages to decorate!

                                +

                       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

                           =====

                              ===

A very happy Christmas and successful and abundant New Year!

 

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