Tuesday, January 1, 2013

Happy New Year 2013

One of the questions that may be asked about our new year is whether 2013 is composite or prime -- that is, whether it does or does not have factors other than 1 and the number itself.  A shortcut useful here is this test for divisibility by 3 (offered as a 5x5 square):

        An integer is
        divisible by
        3 if and only
        if the sum of its 
        digits is also.

And so, since 2 + 0 + 1 + 3 = 6 (which is divisible by 3), then 2013 is divisible by 3.  Indeed, the prime factorization is 2013 = 3 x 11 x 61.

My email on this New Year's morning contained a gift -- "Digits" -- a poem that compares numbers with nature, from Virginia poet and dream specialist Joan Mazza;  she has given me permission to post it here. 

     Digits     by Joan Mazza 

     A second look at the oldest fossils
     of early vertebrates and you’ll see

     seven digits, or eight, not five. Devonian
     tetrapods all had more than five digits

     ending their primitive limbs. In evolution,
     who wins the lottery of millions

     of descendants in the future family
     tree, instead of extinction’s blind end,

     may only catch a bit of luck, not always
     adaptive advantage. Let’s count

     ourselves fortunate that our number
     systems aren’t based on fourteen

     phalanges, instead of base ten. Just
     calculate how differently we’d measure

     everything. Called a TEN, you’d
     be barely average. No prize. Those

     with only five would hide hands
     and feet, afraid of being cast aside

     by others’ pointing and whispers,
     shunned, confined to reside in small

     and separate villages with their kind,
     to wear their narrow shoes and gloves.

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