Geometry of Kindness . . . Power of a Circle

      Found on Facebook recently -- this snapshot of my syllable-count triangle from an earlier blog posting  . . . I like the way that choosing words that conform to a pattern stimulates my thoughts.

From a blog posting back in 2018

An infinite design -- in a poem

Like a circle, the "lazy 8" or infinity symbol -- shown below --never ends.

Recently it was a delight to me to find -- here in the Harpy Hybrid Review -- the following diagram-poem by Philip Wexler entitled "INFINITY".   And I have enjoyed reading and rereading -- exploring the ways that shape and meaning intertwine.

Geometry and Sewing

     The mathematical ideas that I have mastered over the years spread out and infiltrate whatever I do and experience -- when the newspaper carrier throws my bagged Washington Post newspaper on the the porch in front of my second floor door, I wonder -- is the paper's curved path an arc of a circle, or a parabola?  Or ??? 

     Today, as I was sorting old newspapers and magazines into piles for saving or recycling or trashing, my items-to-sort included lots of copies of The New Yorker -- and the issue from May 16, 2022 had a page marked;  I opened it to find the poem "FEATHERWEIGHT" by Chase Twichell.   This poem reminded me how much my sewing activity connects to mathematics.  I offer below the poem's opening stanzas -- followed by a link to the complete poem online (both print and audio versions).

        FEATHERWEIGHT     by Chase Twichell

            At fourteen, I taught myself to sew
            on a Singer Featherweight,

A Lecture on the Cube

     Summer weeks spent teaching English to Romanian students have helped me to learn of several of the country's fine poets and to get involved in a bit of translating.  Romanian mathematics professor, Gabriel Prajitura (now at SUNY Brockport) -- whom I first met at Pennsylvania's Bucknell University when I was teaching nearby at Bloomsburg University -- worked with me to translate several mathy poems by Nichita Stanescu (1933-1983).  The Summer/Autumn 2004 issue of Circumference:  Poetry in Translation included "A lecture on the cube" and "A lecture on the circle."  My blog posting on April 18, 2014 -- available at this link -- shares "A lecture on the circle" -- and I offer the other below:

     A lecture on the cube     by Nichita Stanescu

        You take a piece of stone,
        chisel it with blood,
        grind it with Homer’s eye,
        burnish it with beams
        until the cube comes out perfect.       

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.

In Praise of the Irrational

     Japanese-American poet and retired math teacher Amy Uyematsu recently has published a new poetry collection, That Blue Trickster Time (What Books Press, 2022) and she has given me permission to share this fascinating mathy poem -- which vividly links the mathematical with the personal --  from that collection.

   In Praise of the Irrational     by Amy Uyematsu

        :  Kanpai (that's Japanese for “cheers”)

       Hooray for the illogical,
       this tale of built-in contradictions,
       each perilous paradox that can
       drive us bananas – and the curious
       ways we keep the faith.

       There's a logic to zero –
       ask any mathematician, poet or priest -
       but don’t expect them
       to explain.

       There's a profound dependability
       in the irrational instincts
       of women – yes us – all
       tenderness, guts, and a fierceness
       no man will ever fathom.  

Mathematics -- not isolated STARS but COMMUNITY

     In his 1940 book-length essay, A Mathematician's Apology, eminent British mathematician G. H Hardy minimizes the importance of those who communicate mathematics to those outside the research community   ... the book's opening paragraph is show below . . . it concludes with "Exposition, criticism, appreciation. is work for second rate minds."

The complete essay is available online here

Stories of Quadrilaterals

     Sometimes I have time to browse my shelves and rediscover old favorites.  Several of this blog's much-read poems have come from Scottish author Brian McCabe (Find blog search results at this link) -- and below I offer the first part of McCabe's two-part poem ("Two Quadrilaterals") entitled "The Restless Square."

Two Quadrilaterals    by Brian McCabe

     Part 1.  The Restless Square  

          There was a square who yearned
          to become something else.

          It stretched its legs to mimic
          an elegant rectangle but
          lost its balance, leaned over
          in a perilous parallelogram.    

Equation Poetry

     The term "Equation Poetry" is the title of an article by Radoslav Rochallyi  -- and posted on 11/9/ 2021 here in the MATH VALUES blog.  Rochallyi is a poet, essayist, and interdisciplinary artist living in Prague, Czech Republic and author of eight books of poetry.   For Rochallyi, "mathematical" poetry is not poetry about mathematics but poetry whose form is determined by a mathematical rule. 

     For example, he uses the formula for the area of a circle --  a = π r²  --  to form this example of Equation poetry:

     And, from the binomial formula,    

 

if we let x = time, a = being, n = now, and k = know -- our binomial formula becomes this poem:

 

 

Visit Rochallyi's article at this link to learn lots more. 

 

Looking back . . . to previous posts . . .

  BROWSE and ENJOY!

Back in January 2020 I gathered a list of titles of previous posts and posted it here at this link.  And below I offer titles of postings -- with links -- since that time.

And, if you are looking for a post on a particular topic,
you are invited to explore the SEARCH feature in the right-hand column
OR to browse the list of  Labels (also to the right) -- and click on ones that interest you.

 

TITLES OF POSTS (with links) 

June, 2021    

      Math Communication with Poetry -- Strogatz Prize

      One More Love Poem

      Interpreting Khayyam -- in Rhyme   

      Putting CALCULUS into a poem . . .  

      Images of a Complex World   

      Encryption and Love   

      Every Seventeen Years . . .   

      A Life Made to Count   

      A Few Lines of Parody   

      Euclid and Barbie -- and attitudes toward math . . .

 

May, 2021      

      A Mathy Rhyme from Twitter   

      A Rhymer and an Analyst -- a Friendship   

      What does CANCEL mean? -- some poetic wordplay!   

      MoMath Celebrates Limericks!  

      Reflecting on Pi . . .   

      Keeping Track of Chairs   

      Mathematical Forms in Poetry . . .  

      Mathy Jokes    

      Climate Concerns   

      Celebrate Math-Women -- Celebrate AWM  

A Few Lines of Parody

      Recently I re-found -- in my copy of The Mathematical Magpie by Clifton Fadiman (1904-1999)  (Simon and Schuster, 1962) -- these lines by Lewis Untermeyer (1885-1977):

    EINSTEIN:  A PARODY IN THE MANNER OF EDW-N MARKH-M

    We drew our circle that shut him out,
    This man of Science who dared our doubt.
    But ah, with a fourth-dimensional grin
    He squared a circle that took us in.

Untermeyer's lines first appeared in his Collected Parodies.    Here is a link to a second edition (1997) of The Mathematical Magpie (for which the title page description includes:  stories, subsets of essays, rhymes, anecdotes, epigrams . . . rational or irrational . . .)

Reflecting on Pi . . .

     A few months ago I got an email from Adaobi Chiemelu, a Nigerian poet and spoken word artist who studied studied mathematics at the University of Nigeria.  Recently Adaobi has sent me one of their poems -- about division and infinity and pi and . . . 

Dividing Together     by Adaobi Chiemelu

The cake was holy communion
You picked one piece not fatter than your two fingers
You smiled
You watched as the next person went on to do same 
          and put the same in their mouth
You thought of pi     

TEACHERS are important ... enlarge Hardy's view!

     One of the classics written about mathematics is G. H. Hardy's 1940 book-essay, A Mathematician's Apology -- a treatise that gives valued insights into the nature of mathematics, its beauty, and the roles of mathematicians.   But today I want to urge us all to enlarge Hardy's view (shown in the box below) which offers scorn for those who talk ABOUT mathematics instead of creating it.  Our teachers and the others who spread mathematics out into the world ALSO are vital.

    Let us use geometry as Edwin Markham does -- and include

in the important world of mathematics those persons who communicate about that world.

          Outwitted     by Edwin Markham (1852-1940)

          He drew a circle that shut me out--
               Heretic, rebel, a thing to flout.
          But Love and I had the wit to win:
               We drew a circle that took him in!

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.

Inclusion-Exclusion -- the power of the CIRCLE!

On my mind today, this poem by U.S. poet Edwin Markham (1852-1940):

          Outwitted     by Edwin Markham

          He drew a circle that shut me out--
               Heretic, rebel, a thing to flout.
          But Love and I had the wit to win:
               We drew a circle that took him in!

Find more of Markham's work here.

SUNSET poem -- guided by a Fano diagram

GEOMETRY IN POETRY

Warning:  even if you are not a mathy person, you will like the poem offered below!

     When a writer picks up her pen and starts to write, the initial phrases may be simply a ramble -- a pouring out of thoughts that might be able to be shaped into a poem.  Over the centuries, writers have used syllable-counts and patterns of rhyme to help them shape their word into the best-possible expressions.
     Earlier in this blog (in this 2016 posting) is a poem created by Black Hills State University mathematician Daniel May using a geometric structure called a Fano Plane.  I offer below another similarly-structured creation by May -- and, after the poem, a bit of explanation.

Fano Plane diagram

Sunset : October 11th      by Daniel May

it's late in the day and we’ve climbed up this rise.
i stare, too closely, into the
leaving of the light streaming through the treetops 
          from the next ridge over.

later, i'll wonder if looking into the sun makes me crazy,
or gives me secret terrible knowledge.
my last willful act will be staring directly into our star, 
          and it will be like burial at sun.

Qatar teacher uses Arabic poetry to teach math

     Today I call your attention to an inspiring story -- Mohamed al-Janahi is an engineer-turned-elementary-school-math-teacher who uses Arabic poetry to help students understand mathematical concepts.  More of this story is found here,   In Arabic, in this YouTube video, al-Janahi tells of his work.
     And to add a bit of poetry in English, I offer a couple of stanzas of "Time" from my collection My Dance is Mathematics (now out of print but available online here).

from   Time       by JoAnne Growney

                  I

          The clock goes round —
          showing time a circle
          rather than a line.
          Each year's return to spring
          swirls time on time.  

Sailboat Mathematics

     Celebrated on June 2 at the Joaquin Miller Poetry Series Washington DC's Rock Creek Nature Center, poetry by winners of the  Jacklyn Potter Young Poets Competition, sponsored by The Word Works, Inc.  One of these winners, Julien Berman, is a student at Georgetown Day School and a prize winning writer and accomplished violinist AND a member of the GDS Math team.
     Here is Julien's winning poem:

Sailboat Mathematics     by Julien Berman

A stretched canvas tarp
Not ungainly in style, but again not cut in a perfect polygon.
A wooden beam or two
Slung upwards and out, at ninety degrees.     

Have fun with "The Pi Song"

     Often we celebrate the number pi -- ratio of the circumference of a circle to its diameter, an infinite non-repeating decimal that begins with 3.1415926535 8979323846 2643383279 . . ..  Pi is a bridge between day-to-day mathematics that nearly all of us know and mathematics that is complex and difficult. 
     My own celebration of Pi includes these earrings -- but I have friends and former colleagues in the Bloomsburg University Department of Mathematics and Digital Sciences that celebrate Pi in a far more entertaining way -- in song.  Here is a link to the YouTube version of "The Pi Song" with lyrics by Bill Calhoun and Kevin Ferland and performed by "Professor Parody (Kevin Ferland).  Performance credits are found here.  And here is a link to some more details about the song.

Here is a link to a previous posting with more mathy song lyrics by Bill Calhoun.

All Numbers are Interesting . . .

     For math poetry and math art and a host of enticements to love math if you don't already, I recommend a visit to Grant Sanderson's website 3blue1brown.   Here are the opening stanzas of one of his fascinating poems:

       Moser's Circle Problem

       Take two points on a circle,
       and draw a line straight through.
       The space that was encircled
       is divided into two.

       To these points add a third one,
       which gives us two more chords.
       The space through which these lines run
       has been fissured into four.
           . . .

Read all of this poem AND watch a video here.

And here is a link to "All Numbers are Interesting."