A Diagonal . . . and so little time . . .

On my mind in recent days is the problem of "so little time."  About a year ago I posted a wonderful mathy poem by Californian Brenda Hillman about time.  The complete poem is available here; below I supply the opening lines:

       Time Problem     by Brenda Hillman

               The problem
                of time.      Of there not being 
                enough of it. ...

Over the six years of this blog, the most-visited post has been "Varieties of Triangles"  with poetry by Guillevic.  Here is another of that poet's charming geometric offerings:

 Diagonal   by Guillevic  (Englished by Richard Sieburth)

       To get where I have to go
       I claim right of way.

       Because I provide communication
       Between two angles

       I take precedence
       I take up residence.

       I cross first,
       Come what may.
 
"Diagonal" is found in Guillevic's Geometries,from Ugly Duckling Presse (2010). Buy it!

"The Computation"

     Here is a favorite poem of mine -- and it available with many others in the anthology, Strange Attractors:  Poems of Love and Mathematics (A K Peters, 2008), edited by Sarah Glaz and me.

     The Computation     by John Donne (1572-1631)

     For the first twenty years, since yesterday,
     I scarce believed thou couldst be gone away,
     For forty more, I fed on favours past,
         And forty on hopes, that thou wouldst, they might last.
     Tears drowned one hundred, and sighs blew out two,
         A thousand, I did neither think, nor do,
         Or not divide, all being one thought of you;
         Or in a thousand more, forgot that too.
     Yet call not this long life; but think that I
     Am, by being dead, immortal; can ghosts die?

How clever of Donne, writing all those years ago, to speak (indirectly, at least) to 2016's Math Awareness Month theme, "The Future of Prediction."

The Future of Prediction

     As well as being National Poetry Month, April is Mathematics Awareness Month and this year's theme is "The Future of Prediction."  In search of a poem on the theme, I found the following sonnet by poet Joyce Nower -- third in a section of 20 sonnets, "Meditations of Hypatia of Alexandria," in her collection, The Sister Chronicles and Other Poems (IUniverse, 2012), available in both print and electronic versions.

3.  Scales Can't Calculate*     by Joyce Nower

       Hypatia, Math, God One, can't plot the locus
       of soul and star, predict exactly where
       and when you die, whose hand deals death.  No hocus

Contemplating the heavens

English writer G. K. Chesterton (1874-1936) was a poet but was better known for his pithy sayings.   For example, we have the following statement (originally found here). 

         The
         difference
         between the poet
         and the mathematician
         is that the poet tries to get
         his head into the heavens
         while the mathematician
         tries to get the heavens
         into his head.

     Alas, Chesterton's comment obeys the common assumption that the male pronoun should be used for mathematicians.  Another poetic comment on mathematicians is found in a poem by Anthony Hecht -- "Mathematics Considered As a Vice" -- available here at PoetryFoundation.org.  Hecht's poem  offers a strongly negative view of the abstract nature of mathematics.
     Rivalry between mathematics and poetry comes to a head in April -- during which we will celebrate both "National Mathematics Awareness Month" and "National Poetry Month."

The Shape of the World -- a dream of equality

     One of the most vital components of the Washington DC poetry scene is Split This Rock -- an  organization that speaks and acts against injustice.  (Co-founder and Executive Director, Sarah Browning, is a long-time activist and a fine poet.)  One of STR's 2016 programs has been Al-Mutanabbi Street Starts Here DC 2016,  a book arts and cultural festival that commemorates the 2007 bombing of Baghdad’s historic bookselling street, and emphasizes free exchange of ideas and knowledge, in solidarity with the people of Iraq.  Several weeks ago at one of these events I met poet Dunya Mikhail and her translator, Kareem James Abu-Zeid, and was involved in discussion and reading from The Iraqi Nights (New Directions, 2015).  Here is a mathy poem from that collection.

       The Shape of the World      by Dunya Mikhail
                                           translated from the Arabic by Kareem James Abu-Zeid)
       If the world were flat
       like a flying carpet,
       our sorrow would have a beginning
       and an end.

       If the world were square,
       we'd lie low in a corner
       whenever the war
       plays hide and seek.

       If the world were round,
       our dreams would take turns
       on the Ferris wheel,
       and we'd all be equal.

     A link to the Arabic original version of this poem is shown at the bottom of Mikhail's webpage -- a link that also offers  a recording of her reading this poem, set to music.
     And please note that coming up soon is the  2016 Split This Rock Poetry Festival (April 14-17, 2016) with many excellent workshops and readings.  Learn about it here and register (online registration closes March 31).  See you there.

World Poetry Day -- Celebrate favorites!

     Down, down, down into the darkness of the grave
     Gently they go, the beautiful, the tender, the kind; 

     Quietly they go, the intelligent, the witty, the brave.

     I know. But I do not approve. And I am not resigned.

                      From "Dirge without Music" by Edna St Vincent Millay; offered by Hermann Weyl

                      in a Memorial Address for Amalie "Emmy" Noether on April 26, 1935 at Bryn Mawr College.

Poems that Count

On January 6 of this year I attended a wonderful poetry reading (sponsored by The Word Works) that featured the work of poets Tera Ragan and James Ragan (Tera's father). Their poetry is rich in imagery of their birthplaces -- near Pittsburgh -- and Czechoslovakia (where James' parents were born and a place they visited often).  Please enjoy these lovely and varied poems that include a few well-chosen numbers:   "Alcove" by Tera Vale Ragan; "Beckett Had Only One Student" and "The Eskimo's Twelve Expressions of White" by James Ragan.
                                                               
       Alcove     by Tera Vale Ragan

       Brick upon stone, a growing
                                        foundation,
       he builds a new family home up
       from the ground
                                        cement and marble
       tile to ceiling
       beam and red oak
                                        he paid for with cash.

A poem is an equation?

     Exiled Romanian poet Nina Cassian (1924-2014) spoke with a daring and imaginative voice that I have much admired.  And she occasionally used mathematical imagery in her work -- as in the following poem:

Controversy   by Nina Cassian
                                          (translated from Romanian by William Jay Smith)
I wrote a poem, an oblique poem,
a kind of calligram, I mean.
Someone said it was an equation
being solved behind a screen. 

Celebrate Math Women

     March is Women's History Month and, although this year's theme focuses on women in public service and government, my own thoughts tend toward women in mathematics.  My post on July 21, 2015 focuses on math women -- and a google search of the blog using "math women" will lead to a host of additional poems and links.  Enjoy!
     To celebrate math-women one must first be able to name them; here is a link to an important and relevant article by Judy Green, "How Many Women Mathematicians Can You Name?"

I am the girl voice,

Drafts scribed--thoughts stretched, smoothed, squared, sighed --

Catch here now my I.

    

Inspired by Pi

     Last year, a few days after Pi-Day, my email had a link (Thanks, Paul Geiger!) to an example of Pilish -- this one a circle poem by Mike Keith that represents the initial 402 digits of Pi  -- and I have, at last, posted the poem below.  Keith's poem first appeared in the The Mathematical Intelligencer in 1986. 

     And here is a link to musical Pi --at the webpage of "The Derivatives" are math parodies written and performed by Bloomsburg University professors William Calhoun, Kevin Ferland, and Erik Wynters, including The Pi  Song (also known as 3.14159/Circle).

Arnold diffusion (and poets of Romania)

     I have had the good fortune to attend two BIRS Math / Creative Writing workshops in Banff (most recently in January 2016) and one of the organizers of these workshops has been Florin Diacu, a Romanian-Canadian mathematician-poet at Canada's University of Victoria. (For a bit more about my interest in Romanian poets, you may visit this posting from 2012 ; for still more, use "Romania" as a blog-search term.)
     Recently I discovered the following poem by Florin in the January 2014 issue of the Journal of Humanistic Mathematics and that online journal's open-access policy permits me to offer it here.  I have wondered whether it is prudent of me to present a poem about Arnold diffusion, a topic about which I have scant mathematical background.  But I like it, even though my understanding is incomplete; I hope you like it too.

The Marvelous Arithmetics of Distance

     Audre Lorde (1934-1992)  is one of my favorite poets; links to my previous postings of her work in this blog are given below.  Here is the opening poem from one of Lorde's collections, The Marvelous Arithmetics of Distance.

     Smelling the Wind       by Audre Lorde

     Rushing headlong
     into new silence
     your face
     dips on my horizon
     the name
     of a cherished dream  

Links to Favorites

     According to Google, these posts are the top ten favorites of visitors to this blog in the six years since my first posting in March, 2010.  Perhaps you will want to visit one of them.  Or use the SEARCH box to find something favorite of your own.   I invite your comments.  Which posts do you especially like?

Varieties of triangles -- by Guillevic     Oct 13, 2010

     Loving a mathematician (Valentine's Day and .. .)     Feb 12, 2011  

          Rhymes help to remember the digits of Pi     Sep 2, 2010

               "Mathematical" Limericks     Mar 29, 2010

                     Ray Bobo's mathematical poem Jul 14, 2010 
Poems of set paradox and spatial dimension   Feb 22, 2011
     Poems of Calculus   Apr 23, 2010

          Primes and a paradox   Aug 14, 2015
               Theorem-proof / Cut-up / poems   Nov 11, 2010
                     A Fractal Poem   Dec 28, 2014 

Newton, Einstein, Gravity, Poetry

     Recent discovery of gravitational waves has put Einstein (1878-1955) -- and even Newton (1643-1727) -- into recent news, and a visit to one of my favorite reference collections, James R. Newman's four-volume collection, The World of Mathematics, finds those two giants celebrated in verse:

Introductory quotes for Section 21 ("The New Law of Gravitation and the Old Law" by Sir Arthur Stanley Eddington) of Part V (on page 1073 of Volume Two) of James R. Newman's The World of Mathematics.

     Here are links to information about the poets named above:  Lord Byron (1788-1824),  Alexander Pope (1688-1744), and Sir John Collings Squire (1884-1958) -- and these links lead to previous blog postings that feature The World of Mathematics:  March 22, 2011 and August 2, 2011.

Euler formula poem

     Sometimes I try to write a poem that explains a mathematical concept -- it's a difficult task  My effort usually results in something that sounds more like a textbook paragraph than a poem.  And I was thereby hugely delighted (following a lead from Colm Mulcahy) to discover this poem by Grant Sanderson that has fun with a famous mathematical formula due to Euler:

e^iπ + 1 = 0     or, stated differently      e^iπ = -1

Euler Formula    by Grant Sanderson 

Famously
start with e,
raise to π
with an i,
we've been taught
by a lot
that you've got
minus one.

How Old Is the Rose-Red City?

     Most of Martin Gardner's fans are avid puzzler's -- my connection with him is also one of admiration (he was a thoughtful person who was a master at making connections among disparate things) but we are connected via poetry, including topics such as counting all possible rhyme schemes for a given stanza and the constraint-based poetry of OULIPO . . ..
     Gardner (1914-2010) was not a poet -- although he penned a quatrain or two, his great contribution was collecting and publicizing parodies and puzzle-verses by others.  Here is a link to Gardner's collection of poetic parodies, and here is a link to many of Gardner's puzzles, including the stanza below, "How Old is the Rose-Red City?" 

Visit JHM for Mathy Poems

     Today I'd like to direct you to the Journal of Humanistic Mathematics, an online open-access journal that features poetry in each issue.  The Table of Contents for the first issue of 2016 is now available here -- and I offer below a poem from Issue 1 of 2015.  (Before sharing the poem "Prisoner's Dilemma" by Raymond Greenwell I want also to mention that JHM is looking for investigative journalists and that today's "Poem of the Day" at Poets.org is "Evolution" by Linda Bierds and inspired by the work of Alan Turing.)
     I am particularly intrigued by Greenwell's poem because the Prisoner's Dilemma is a decision model close to my concerns about the environment. (More comments below.)

       Prisoner's Dilemma     by Raymond N. Greenwell

       Your best choice is my demise.
       My wise choice is your defeat.    

Using a Fano plane to create a poem

     South Dakota mathematician Daniel May enjoys finding connections between his discipline and other arts -- and herein we consider a constraint-structure for poetry that he has developed using a Fano plane.  In brief, a Fano plane (shown in the diagram below) consists of 7 points and 7 lines (the three sides of the triangle, the three altitudes of the triangle, and the circle) -- with each line containing 3 of the points. 

Fano Plane Diagram

May creates a poem by associating a word with each point of the Fano plane and then creates a three-line stanza for each line of the diagram.  Here is a template for the poem "adore" -- and the poem itself is offered below the diagram: 

Visiting the Australian Poetry Library

     An Australian poet (Erica Jolly) whom I have met through this blog has helped me to learn about the great variety of poetry and related activities that are available on her continent  -- and today I want to link you to the Australian Poetry Library and to offer a mathy poem by Peter Goldsworthy that I enjoyed there.

     1     by Peter Goldsworthy 

       Arithmetic divides 
       and rules the world,
       freezing the flow
       in single frames,
       colourising each
       by numbers.

A sonnet for Napoleon's Theorem

     In geometry, Napoleon's theorem (often attributed to Napoleon Bonaparte, 1769–1821) states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the centers of those equilateral triangles themselves are the vertices of an equilateral triangle.  In a 2015 lecture at the  University of Maryland,  mathematician Douglas Hofstadter (perhaps best known for Godel, Escher, Bach: an Eternal Golden Braid -- Basic Books, 1970) presented Napoleon’s theorem by means of a sonnet.  Perhaps you will want to have pencil and paper available to draw as you read:

Napoleon's Theorem     by Douglas Hofstadter

Equilateral triangles three we’ll erect
Facing out on the sides of our friend ABC.
We’ll link up their centers, and when we inspect
These segments, we find tripartite symmetry.

Rabbis should learn to solve quadratics

     Thanks to mathemagician Colm Mulcahy who connected me with poet Lisa Dordal -- and thanks to her for permission to offer these lines, entertainingly seasoned with math words:

Why Rabbis Need to Know
How to Solve Quadratic Equations  

                                         by Lisa Dordal (with help from Laurie Samuels)

Because they are good exercise
for your logic muscles, which you’ll need
to work through those pesky J says-P says conflicts of text –- 
the bumpy remains of a Torah affair. 

Tartaglia solving the cubic -- in verse

     Mathematical historians now credit both Cardano and Tartaglia with the formula to solve cubic equations, referring to it as the "Cardano-Tartaglia Formula." Tartaglia is known for reporting solutions of three different forms of the cubic equation in a poem (1534).  Below we offer Boston poet Kellie Gutman's English translation of Tartaglia's verse, followed by the original Italian.

When X Cubed    by Niccolò Tartaglia (1500–1557)       (Englished by Kellie Gutman)

When x cubed’s summed with m times x and then   
  Set equal to some number, a relation    
  Is found where r less s will equal n.

Now multiply these terms. This combination
  rs will equal m thirds to the third;
  This gives us a quadratic situation,    

Not good at math . . .

     Connecticut poet Joan Cannon is a senior who laments her lingering anxiety over mathematics in her poem, "Humility," below.  I found Cannon's poem on Senior Women Web and it is accompanied there by selections from an article by Patrick Bahls entitled "Math and Metaphor:  Using Poetry to Teach Mathematics."  The complete article is available here.

     Humility    by Joan L. Cannon

     Archetypes, mysteries, simple clues
     that only fingers and toes, sticks and stones
     and flashes of inspiration require
     for universes to be disclosed ...
     symbols for functions and formulae
     for proof; logic so easy for some —
     why am I innumerate?  

Math Anxiety

     Recent comments from a friend describing anxiety that seems to freeze his attempts to understand and use a new mathematical concept have caused me to recall and dig out this old poem -- and, by recalling it, to increase my understanding of my friend. 

     The Math Teacher's Golf Lesson     by JoAnne Growney

     My practice swing was perfect --  slow start, easy
     acceleration through the ball to finish high.
     "Beautiful," he said.  "It's time to hit a few."
     I addressed a ball and settled down and swung --
     and missed.  "Concentrate," he said.  I squinted

Soon it will be February -- and Valentine's Day

     Looking back:  on February 12, 2011 I posted math-poetry suggestions for Valentine's Day at this link: Loving a mathematician (Valentine's Day and . . . ).   This posting from Feb 9 2013 offers verse along with an animated drawing of a heart-curve --a cardioid.    And this link goes to a mathematically poetic digital art exhibit (that includes a cardioid) by Guang Zhu.   
     For even more poetry related to the love-holiday, enter "Valentine" in the SEARCH box to the right.  Enjoy!

Poetry from a math teacher's son

     In an earlier post I have noted how effectively mathematicians and their mathematics may be described by poets who are in the same family.  This link, too, leads to portraits of mathematicians.
     Poet and novelist John Updike (1932-2009) was the son of a math teacher and the selection below is a sonnet that begins in the style of a math-class word-problem linking his own age with that of his father.

from  Midpoint     by John Updike

     FATHER, as old as you when I was four,
     I feel the restlessness of nearing death
     But lack your manic passion to endure,
     Your Stoic fortitude and Christian faith.
     Remember, at the blackboard, factoring? 

A sonnet for W.R.Hamilton

      Irish mathematician William Rowan Hamilton (1805-1865) was also a poet (see, for example, this sonnet in a prior posting (13 October 2011).  Irish poet and physicist Iggy McGovern has written A Mystic Dream of 4:  A sonnet sequence based on the life of William Rowan Hamilton (Quaternia Press, 2013). 

The collection is prefaced by this quote from Hamilton:

"The quaternion [was] born, 

as a curious offspring of a quaternion of parents, 

say of geometry, algebra, metaphysics, and poetry."

Here is McGovern's opening sonnet.

GEOMETRY     by Iggy McGovern

Once, any pupil could define me best:
"points, lines, angles and figures", could amuse
The table with the Christmas cracker jest
About 'the squaw' on the hypotenuse! 

The world is round . . . or flat!

British poet Wendy Cope frequently includes edgy humor in her poems (she is, indeed, a prizewinner in light verse) -- and I like that.  In the poem below (found at PoetryFoundation.org and originally published in Poetry in 2006), Cope examines arguments of whether our world is flat or round.  Part 2 of the poem involves the interesting permutation pattern that is called a pantoum (Lines 2 and 4 of each four-line stanza are repeated (approximately) as lines 1 and 3 of the next stanza -- and the final stanza is wrapped into the first).

Differences of Opinion     by Wendy Cope

1     HE TELLS HER

He tells her that the earth is flat --
He knows the facts, and that is that.
In altercations fierce and long
She tries her best to prove him wrong,
But he has learned to argue well.
He calls her arguments unsound
And often asks her not to yell.
She cannot win.  He stands his ground.

The planet goes on being round.   

Counting those who grieve . . .

Each day's email brings me a Poem-a-Day from Poets.org and today's selection by Matthew Olzmann considers the tragedies from gun-violence in our news too often these days. Numbers are "objective" -- and count those who watch and grieve as well as the guns and shooters -- or are they?  Here is an excerpt from Olzmann's poem, "Letter Beginning with Two Lines by Czesław Miłosz":

          . . .   Did I say
          I had “one” student who

          opened a door and died?
          That’s wrong.

          There were many.
          The classroom of grief  

Math is Brewing . . .

For one of my granddaughters who likes poems, I recently purchased If You're Not Here, Please Raise Your Hand:  Poems about School by Kalli Dakos (Aladdin Paperbacks, 1995).  It's hard to find school poems that are non-critical of math -- but this one, at least, has some rhyming fun while cooking it.

Math is Brewing and I'm in Trouble     by Kalli Dakos

       Numbers single,
       Numbers double,
       Math is brewing
       And I'm in trouble,

       If I could mix a magic brew,
       Numbers, I'd take care of you.

2015 (and prior) -- titles, dates, links for posts

If you wish to easily BROWSE past postings . . .

Scroll down to find titles and dates and links to postings in 2015.  

OR follow these year-number links to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this blog was begun. At the top of the column to the right is a SEARCH box for the blog and this link leads to a PDF file of searchable topics and names of poets and mathematicians presented herein.  Scrolling down the right-hand column leads to a partial list of LABELS that are linked to a list of blogs that contain them.
   Dec 31  Precision leads to poetry . . .
   Dec 28  Can a woman learn science (or mathematics)?
   Dec 24  And now welcome Christmas . . .
   Dec 22  Let us not forget . . .
   Dec 20  Who put the pie in Pythagoras?
   Dec 18  A student writes poetry for a math class . . .
   Dec 15  Generalized Pythagorean Theorem--a visual poem? 

Precision leads to poetry . . .

As the year ends, a quote from one of my once-favorite authors, Don DeLillo (in correspondence with David Foster Wallace -- whose Infinite Jest is on my to-read list), earlier offered by Jordan Ellenberg in Quomodocumque.

Quoting DeLillo:

          Once, probably, I used to think that vagueness 
          was a loftier kind of poetry, truer 
          to the depths of consciousness, and maybe 
          when I started to read mathematics and science 

          back in the mid-70s I found an unexpected lyricism 
          in the necessarily precise language 
          that scientists tend to use. 
          My instinct, my superstition 
  
          is that the closer I see a thing 
          and the more accurately I describe it, 
          the better my chances of arriving 
          at a certain sensuality of expression.

And at the BrainyQuotes website is this quote (and many others) by DeLillo (and many others).

For me, writing is a concentrated form of thinking.

HAPPY NEW YEAR!

Can a woman learn science (or mathematics)?

It is not a new idea that women do not have scientific aptitude, that teaching them requires special accommodation.  Here, in a poem by one of the greatest scientists of all time, is a description of a condescending lecture to a female student, individually and behind a curtain, followed by her mocking reply.

Lectures to Women on Physical Science  by James Clerk Maxwell  (1831-79)

I.    PLACE. —A small alcove with dark curtains.
       The class consists of one member.
       SUBJECT.—Thomson’s Mirror Galvanometer.

      The lamp-light falls on blackened walls,
            And streams through narrow perforations,
      The long beam trails o’er pasteboard scales,
            With slow-decaying oscillations.
Flow, current, flow, set the quick light-spot flying,
Flow current, answer light-spot, flashing, quivering, dying.

And now welcome Christmas . . .

Let us sing . . .

(a version of)  The Twelve Days of Christmas

          The twelfth day of Christmas.
          My true love gave to me,
          Twelve lords a leaping,
          Eleven ladies dancing,
          Ten pipers piping,
          Nine drummers drumming,
          Eight maids a milking,
          Seven swans a swimming,
          Six geese a laying,
          Five golden rings,
          Four colly birds,
          Three French hens,
          Two turtle doves,
          And a partridge in a pear tree.

To learn some history of this song (and its variations), frequently sung as a cumulative marathon, see Wikipedia.

Let us not forget . . .

At this time of year in the Northern Hemisphere, many are without shelter -- and are cold.  Let us think of them  -- as Cecil Day-Lewis (1904-1972) does in "A Carol" below (a poem whose lines for the most part maintain an alternating 6-5 syllable count and which contains the small number two).  Let us remember to share our warmth.

       A Carol     by Cecil Day-Lewis 

       Oh hush thee, my baby,
       Thy cradle's in pawn:

Who put the pie in Pythagoras?

Irish poet and physicist Iggy McGovern has written both humorous and serious verse.  Today we have lines from him that startle and amuse -- below I present, with his permission, selections from his collection Safe House (Dedalus Press, 2010).  Here are "Belfast Inequalities" and "Proverbs for the Computer Age":

Belfast Inequalities     by Iggy McGovern
                          for Master Devlin
       Who put the pie in Pythagoras,
       who put the bra in algebra
       and who was the first to say: Let x
       be that unknown quantity in sex?
       the answer's in some chromosome
       and not the sums you do at home 

A student writes poetry for a math class . . .

A recent fun experience for me has been correspondence with Melanie Simms, a poet and math student at Pennsylvania's Bloomsburg University, where I taught for a bunch of years.  Melanie recently completed the course "Mathematical Thinking" -- a course that I helped to develop during my years at BU and one for which I wrote a textbook (Mathematics in Daily Life:  Making Decisions and Solving Problems, McGraw-Hill, 1986).   The course was developed to offer general quantitative skills for students majoring in fields (such as English or Art)  that do not have a specific mathematics requirement.  Melanie's instructor for the course, Paul Loomis, is a singer and songwriter and, with him as first reader, Melanie composed a mathematical poem involving course material.  She has shared the poem with me and has given me permission to post it here.

     The Mathematics of Chance      by Melanie Simms

     The gods of chance
     Have left me skewed
     My distribution, variable!
     With ranges far, and ranges wide
     My navigation's terrible! 

Generalized Pythagorean Theorem--a visual poem?

While thinking about my December 13 posting featuring work by Richard Kostelanetz -- visual poetry with numbers -- I was browsing a fascinating book by Ivan Moscovich, The Puzzle Universe:  A History of Mathematics in 315 Puzzles (Firefly Books, 2015) and came to the following diagram.  I offer it as a visual poem. 

In addition to the squares, what other areas constructed on the sides of a right triangle may be correctly summed to give a third area of the same shape?

Visual poems with numbers

     I have a good friend who does not care for the sorts of poetry that are written today.  When I asked what he likes he cited "When I Was One-and-Twenty" by A E Housman (1859-1936) and the sonnet "Ozymandias" by Percy Bysshe Shelley (1792-1822).   My own preferences in poems, on the other hand, are less certain.  I like to explore, to discover what new things may be said within new forms and constraints.  The following selection, "Notes on Numbers" by Richard Kostelanetz, introduces some of the ideas that this artist/writer/critic explores in his visual poetry -- with numbers -- examples of which are available through links offered at the end of this posting.

Notes on Numbers      by Richard Kostelanetz