TRITINA -- a tiny SESTINA

     In several previous postings (collected at this link) this blog has considered the poetry form called a sestina:    a sestina has 39 lines and its form depends on 6 words -- arrangements of which are the end-words of 6 6-line stanzas; these same words also appear, 2 per line, in the final 3-line stanza.

     The American poet Marie Ponsot (1921-2019) invented the tritina, which she described as the square root of the sestina.   the tritina is a ten-line poem and, instead of six repeated words, you choose three, which appear at the end of each line in the following sequence: 123, 312, 231; there is a final line, which acts as the envoi -- and includes all three words in the order they appeared in the first stanza.  Poinsot has said -- and I agree -- poetic forms like the tritina are "instruments of discovery . . . they pull things out of you."  Read more here in an article by poet Timar Yoseloff.)

   

The Geometry of Gerrymandering

gerrymandering: the practice of dividing or arranging 
a territorial unit into election districts in a way 
that gives one political party an unfair advantage in elections

       A recent Scientific American article by Manon Bischoff, "Geometry Reveals the Tricks Behind Gerrymandering," has reminded me of the horrors of this practice.  To express my thoughts about a particular concept, often a stanza that matches mathematical constraints helps me to carefully consider word choices and attempt clear and concise expression. The following syllable-square is a start toward expressing my point of view:

          For fair elections
          voting districts must
          be proportional,
          not maneuvered by
          gerrymandering.

This Scientific American author Manon Bischoff is an editor at Spektrum der Wissenschaft. She primarily covers mathematics and computer science and writes the column The Fabulous World of Mathematics. Bischoff studied physics at Technical University of Darmstadt in Germany and then worked as a research assistant at Johannes Gutenberg University Mainz in Germany.

Mathematical Forms in Poetry . . .

      During recent days, one of my special enjoyments has been finding time to read Marian Christie's blog -- a delightful collection of poetry and poetic musings with frequent connections to mathematics.  Christie's biographical sketch (available here) indicates that she, like me, grew up enjoying both poetry and math.  She became a math teacher and, after her years of teaching ended, she turned her attention to poetry.  Below I present a sample of her mathy poetry, followed by links to several of her postings.

Today, in a season that is approaching summer, I coolly offer Christie's "Midwinter" poem (found here in her blog)  -- a stanza in which the poet uses Pascal's triangle to pattern her words:

a Pascal-triangle poem -- find it and lots of other mathy poems here.

Here, next, are links to several of Christie's math-poetry blog postings.  ENJOY!

Squaring the circle . . . or not . . .

     Start with a CIRCLE -- is it possible, using only a straightedge and compass, to construct a SQUARE with the same area as the starting circle?  This problem, posed by ancient geometers, was long believed to be impossible, but not proven so until 1882 when Ferdinand von Lindemann proved that π is transcendental.
     Freelance editor and math-geek Sam Hartburn offers at her website a fun-to-read poem on this topic.  The first stanza is offered below, followed by a link to the full poem text -- and a recording. 

 (not) Squaring the Circle     by Sam Hartburn

          So I had this circle, but I wanted a square
          Don’t ask why, that’s my affair
          The crucial aspect of this little game
          Is that the area should stay the same
          Ruler and compass are the tools to use
          It’s been proven impossible, but that’s no excuse
          Many have tried it, but hey, I’m me
          I’m bound to find something that they couldn’t see

          So, here we go
                . . .

Hartburn's complete poem (and recording) may be found here.

Enrich Mathematics Classes with Poems

    In my mathematics classrooms, I have found it a challenge to include the history and spirit of mathematics -- and its people -- along with the math topics to be covered.  Because I love poetry -- and also write some -- I gradually became aware of poems that could enrich my classes and I began to incorporate poetry in outside readings and essay topics and class discussions.

Here are links to poems that introduce the lives of four math-women:

     Sophie Germain (1776-1831)

     Florence Nightingale  (1820-1910)

     Amalie "Emmy" Noether  (1882-1935)

     Grace Murray Hopper (1906 - 1988)

And here is a poem about four influential teachers of mine; three of them math-people; three of them women.

Math Anxiety can be a hard topic for student or teacher to bring up -- but airing of views and healing might come from discussion.  Poems to consider include: 

Counting the Women . . .

     Sometimes a professional group or a meeting-agenda or a table of contents contains so few women's names that they are easily counted.  In this syllable-square stanza, I praise the absence of that condition: 

     This stanza and others with similar attitude appear in "Give Her Your Support" -- a poetry-page published recently in Math Horizons.  For the entire collection, follow this link.

Celebrate a Science Woman -- and offer friendship!

      Last weekend's Washington Post used the headline 

  Astronomer celebrated as the 'mother' of the Hubble Space Telescope  

for the obituary of Nancy Grace Roman.  It opens with this sentence:

               When Nancy Grace Roman requested permission
               to take a second algebra course in high school,
               the teacher demanded to know, "what lady
               would take mathematics instead of Latin?"

But Roman persisted in the challenging studies and was not dissuaded by biases.  The obituary quotes an interview from Science magazine in which she said:   

Playing with time

        Here is a poem that plays with the geometry of time -- a poem that first appeared in Mathematics Magazine, Vol 68, No 6 (December 1995), page 288.   Several of my other mathy poems written around that same time were collected in a booklet, My Dance is Mathematics, now out of print but available here on my website.  

       Finding Time     by JoAnne Growney

       Points chase points
       around the circle,
       Anti-clockwise,
       fighting time.
       You know time's a circle,
       rather than a line.          

Problems with no solutions

     The syllable-square stanza is a poetic form I often turn to when scientific terminology gives me little hope of matching traditional patterns of rhyme or rhythm -- counting syllables gives discipline and invention to my word choices, and these are for me essential in writing poetry.
     As a grandparent of school-age children  I am deeply worried about the world they are inheriting.  I want it to offer a healthy environment and safety with vast opportunities for women as well as men.  And my own writing often supports these views.   I encourage readers to use the blog SEARCH to find an assortment of poems on a theme -- such as "girl" or "environment" or  . . . For example, here is a link to postings that include the word opportunity.  Scrolling through that list leads to this posting of Eavan Boland's poem, "Code," which honors Grace Murray Hopper.

     And here is my small, worried square:     

          Square worries

          Unless miracles give
          our earth new resources
          that prove unlimited,
          unchecked population
          growth and climate change are
          problems with no solutions.

Seeing the NEWS in square stanzas

Reading today's Washington Post, a surprising statistic:

               Sharks don't kill
               as   many
               as cows do.
 

In the years 2001 to 2013 in the US an average of 20 deaths annually were caused by cows, 

compared with 1 during each of those years from sharks.

Also, Pope Francis has spoken out, expressing his concerns for our environment:

               Pope Francis,
               like me, sees
               climate change--

               a real
               problem.

Geometry of baseball

Many poems are written of baseball; a few of them involve mathematics --  see the posting for April 9, 2010 for math-related baseball poems by Marianne Moore (1877-1972) and Jerry Wemple; see the posting for September 18, 2011 for one by Jonathan Holden.
     Today I feature the opening stanza from a baseball poem by Pennsylvania poet, Le Hinton.

from   Our Ballpark    by Le Hinton

       This is the place where my father educated us:
       an open-air school of tutelage and transformation.
       This is where we first learned
       to count to three, then later to calculate the angle
       of a line drive bouncing off the left field wall.
       We studied the geometry and appreciated the ballet
       of third to second to first, a triple play.
              . . .

The Girl Who Loved Triangles

     I found this poem by Michigan poet Jackie Bartley when I was browsing old issues of albatross (edited by Richard Smyth) and she has give me permission to post it here.  Like Guillevic (see, for example, this earlier post), Bartley has found personalities in geometric figures.

To the Girl Who Loved Triangles     by Jackie Bartley

          Triangulation:  Technique for establishing the distance between two points
                                      using a triangle with at least one side of known length.

One girl in a friend's preschool class
loves the triangle.  Tanya's favorite shape,
the children call it.  Simple, three sided, at least

one slope inherent, slip-slide down
in the playground of mind.  Tension and its
release.  Sure balance, solid as the pyramids.  The 

A square-root of dead weight . . .

     A poet  I love (Seamus Heaney, 1939-2013, 1995 Nobelist) has died. The NYTimes obituary for Heaney quotes one of my favorites of his poems, "Digging" -- also available at poetryfoundation.org.  Part of what I like about this Irishman's poetry is its design.  Not only do his poems offer musicality of language but they feel carefully constructed -- modeling real world phenomena as mathematical models do -- built with careful attention to structure and detail until varied factors have been erected into in integrated whole.  "Digging" ties together the physical activity of Heaney's father shoveling in the peat bogs of Ireland to his own probing with a pen for words. 

Miroslav Holub -- "what use is it?"

     In earlier postings I have expressed my admiration for the Czech poet Miroslav Holub (1923-1998)  -- a research scientist who also wrote fine poetry.  In a biographical sketch of Holub at poetryfoundation.org, the poet is quoted as saying, " . . . I'm afraid that, if I had all the time in the world to write my poems, I would write nothing at all."   There is no agreed standard for the amount of time  to spend on a creative work.  Many poets devote their full time to their craft;  others fear over-writing and strictly limit their writing and editing.  In each aspect of our lives it is possible to do too much or too little thinking about things.  And so it goes.
      My post on 5 April 2013 linked to several math-related Holub poems.  And here is another; in "Magnetism," Holub focuses on the sometimes-silly, sometimes-practical, sometimes-too-limiting question often put to mathematics or science, "what use is it?"

Magnetism     by Miroslav Holub

Spanish favorites

One of my favorite DC-area poet-people is Yvette Neisser Moreno -- who, besides giving us her own work, is active in translation of  Spanish-language poetry into English, most recently (with Patricia Bejarano Fisher) a Spanish and English edition of Venezuelan poet Maria Teresa Ogliastri’s South Pole/Polo Sur  (Settlement House, 2011).  Although I have not found any mathematical poems by Moreno, I learned from an interview that the Chilean Nobelist Pablo Neruda (1904-1973) is her favorite poet and I therefore present here the geometrically vivid opening opening stanza of Part XI of Neruda's well-known long poem, The Heights of Macchu Pichu: A Bilingual Edition (The Noonday Press, 1966). 

Seeing Distance -- geometry in photography

One of my favorite poem-stanza styles is a syllable-square -- it distributes the weights of the words in a way that pleases me. The poem below has squares of several sizes and I post it as a prior-to-seeing-the-exhibit opposite to my response to photography currently displayed at the Smithsonian American Art Museum -- "Pilgrimage," by Annie Leibovitz. While many photographs, my own in particular, seem particularly flat, such was not the case with these. As if I were wearing special lenses, I was able to see and feel depth – not only in a view of Niagara Falls but also in the fabric and buttons of a dress that had belonged to Emily Dickinson.

Permuting words and and enumerating poems

Caleb Emmons teaches mathematics at Pacific University.  Here is his very-clever description of the requirements for a poem to be a sestina -- spelled out in a poem that is itself a sestina.  (A sestina has 39 lines and its form depends on 6 words -- arrangements of which are the end-words of 6 6-line stanzas; these same words also appear, 2 per line, in the final 3-line stanza.) 

9 9-square stanzas

In the current (March 21, 2011) issue of The New Yorker (pages 46-47) may be found the poem "Green Farmhouse Chairs" by Donald Hall.  Hall's fine nostalgic poem consists of 9 stanzas; each stanza is "square" -- and has 9 lines with 9 syllables per line.   Enjoy!

From 2010 -- titles and dates of posts

List of postings  March 23 - December 31, 2010
A scroll through the 12 months of titles below may lead you to topics and poets/poems of interest. Also helpful may be the SEARCH box at the top of the right-hand column; there you may enter names or terms that you would like to find herein.
    Dec 31  The year ends -- and we go on . . .
    Dec 30  Mathematicians are NOT entitled to arrogance
    Dec 28  Teaching Numbers
    Dec 26  Where are the Women?
    Dec 21  A Square for the Season
    Dec 20  "M" is for Mathematics and . . .  

New poems from old -- by substitution

Poet Lee Ann Brown was the featured poet at the November, 2010 Conference on Constrained Poetry at UNC Ashville; this conference celebrated the 50th anniversary of the founding of Oulipo.  In a poetry sampler archived from the Boston Review, we find "Pledge" (see below) and other samples of Brown's work.  Recordings are available at Penn Sound.