Ending the Year with Gratitude -- for Teachers!

     During his time as Poet Laureate of the United States, Billy Collins created Poetry 180 -- a project designed to encourage students to engage with poetry but providing a poem (accessible for high school students) for each of the 180 days of the school year.  Each week in my email, I get a message with links to five of these poems; one of the recent ones (poem 72, given below) has reminded me about the importance of teachers in my life -- teachers of poetry AND teachers of mathematics -- in shaping my learning and my personhood.   Here is  "Gratitude to Old Teachers" by Robert Bly:

   Poem 072: Gratitude to Old Teachers    by Robert Bly

          When we stride or stroll across the frozen lake,
          We place our feet where they have never been.
          We walk upon the unwalked. But we are uneasy.
          Who is down there but our old teachers?

          Water that once could take no human weight—
          We were students then—holds up our feet,
          And goes on ahead of us for a mile.
          Beneath us the teachers, and around us the stillness.

Bly's poem is from his collection, Eating the Honey of Words, (HarperCollins, NY, 1999).  Its presentation in Poetry 180 may be found at this link. 

Here is a link to previous mentions of "Poetry 180" in this blog.

A Cone with a Sphere on top

      The phrase used as title for this post, "A cone with a sphere on top" -- from a slightly-mathy poem by Katharine O'Brien (1901-1986), "Einstein and the Ice Cream Cone" -- has caused me to visualize a Christmas tree and so, in this holiday season, I offer it to you.  Enjoy!  And Happy Holidays!

     Einstein and the Ice Cream Cone     by Katharine O'Brien

     His first day at Princeton, the legend goes,
     he went for a stroll (in his rumpled clothes).
     He entered a coffee shop --- moment of doubt --
     then climbed on a stool and looked about.
     Beside him, a frosh, likewise strange and alone,
     consoling himself with an ice cream cone.   

Counting On . . .

     I was the oldest, the "responsible" one -- when I wanted to sleep in, my mother said, "Your father -- and our farm -- are counting on you."  Here is a bit of my poetic reaction:

     COUNTING ON

        One
        Two   two
        Three   three   three
        Four   four   four   four
        Five   five   five   five   five
        That's how it was growing --
        growing up
        on the farm
        milking cows
        gathering eggs
        scattering grains of corn
        for hens --
        counting   counting   counting . . .
        counting on.

Here is a link to several previous blog posts with poems related to COUNTING.

Patterns of the Wind

     Sometimes a poem contains just a sample of mathematics -- but a very memorable one.   Such is the case with "I Like the Wind" by Robert Wrigley in the 6 September 2010 issue of The New Yorker.  I offer below its opening lines.

       We are at or near that approximate line
       where a stiff breeze becomes
       or lapses from a considerable wind,
       and I like it here, the chimney smokes
       right-angled from west to east but still
       for brief intact stretches
       the plush animal tails of their fires. 

  (The poem continues here for 34 more lines.)

Short Poems

         Poetry, like mathematics, uses condensed language -- often saying quite a lot in just a few symbols.

          POEM     by Aram Saroyan 

          One two
          three there
          are three are
          never seen
          again.                 (from Complete Minimal Poems, Ugly Duckling Press, 2007)

          REFLECTIONS ON AN AMISH CHILDHOOD    by Billy Collins 

          I was
          a little square
          in a round hat.              (from Musical Tables,  Random House, 2022)

This link leads to a previous blog posting with a short (14 syllables) poem of mine AND
with links to poems celebrating five female mathematicians.

Writing -- a Path toward Knowing

     Advice for my grandchildren -- in the form of a Fib.  (Wish I had remembered to give it on November 23 -- which is Fibonacci day. ) 

 

    1            When

    1            I

    2            want to

    3            understand

    5            something difficult

    8            I grab my pen, write about it.

     I'm not sure when I made the discovery but by the time I was in graduate school  I knew that my learning pattern involved my fingers and my pen.  I copied definitions into a notebook, sometimes trying to rephrase them in my own words.  I elaborated the proofs of theorems . . . my fingers helped me remember.

November 23 is celebrated as Fibonacci day because when the date is written in the mm/dd format (11/23), the digits in the date form a Fibonacci sequence: 1,1,2,3. A Fibonacci sequence is a series of numbers where a number is the sum of the two numbers before it.  A Fib is a tiny poem whose lines have as syllable-counts the first 6 Fibonacci numbers.  

For more Fibonacci-related poems, follow this link. 

All Together -- Humor, Math, Poetry

     Blogger and teacher Sue VanHattum (blogger at Math Mama Writes) has been a frequent and valuable contributor to this blog -- find stuff at this link -- and Sue has recently alerted me to a poetic posting that she found on Facebook -- written and drawn by artist-illustrator (and orthodontist) Grant Snider whose pithy and entertaining words and pictures are found at the website Incidental Comics.  Here is the opening portion of that visual-comic-poetic posting:

Opening lines of a visual poem by Grant Snider

Snider's complete "How To Be a Triangle" is found in Incidental Comics at this link.  Another recent posting -- "How to be a circle" -- is found at this link.

Poetry of Mathematics--David Eugene Smith, 1926

      Recently poetry-fan and occasional versifier Greg Coxson, a Research Engineer in the Department  Electrical and Computer Engineering at the US Naval Academy, sent me a link to an essay by mathematician and teacher David Eugene Smith (1869-1944) -- published in The Mathematics Teacher in 1926 and entitled THE POETRY OF MATHEMATICS.  Greg has been, over the years of this blog, a valuable contributor of information about mathy poems and poets -- and some poetry of his own.

     Early in the essay, Smith quotes Thoreau:

We have heard much about the poetry of mathematics, but very little of it has yet been sung.  The ancients had a juster notion of their poetic value than we.  The most distinct and beautiful statements of any truth must take at last the mathematical form. 

     Lots of quotes and viewpoints are offered in Smith's essay and, at the end he speaks of the role of teachers " . . .  mathematics may become and does become poetry in the enthusiasm of an inspired and an inspiring teacher."

The Secret Sits     by Robert Frost (1874-1963)

               We dance round in a ring and suppose,
               But the Secret sits in the middle and knows.

Lots more of Frost's words are available here.