Explore a new idea by writing a poem . . .

      Often I try to unravel the intricacies of a new idea by writing -- using communication with my fingers as steps toward understanding.  And when I found the poem below (here at the website VIA NEGATIVA) I saw it also as a poem of discovery -- and I offer it to you:

Every Line Intersects the Line
                           at Infinity at Some Point                       by Luisa A. Igloria

"Out of nothing I have created a strange new universe."   - János Bolyai (1802-1860)

The optometrist asks you to look into 
the autorefractor: two dark lines form 

a road that stretches from where you sit
to a red barn at the horizon. If your brain 

tells you that you're looking at a point 
at infinity rather than just mere inches away, 

it helps the eyes focus. Things have to end 
somewhere, don't they? In projective geometry, 

Where Will the Parallels Meet?

      One of my favorite poets -- with a varied selection of mathy poems -- is the Czech poet Miroslav Holub (1923-28), an immunologist as well as a poet and one who also wrote about the horrors of World War II.

     Here is one of his poems that I gathered in this 2001 collection Numbers and Faces:  A Collection of Poems with Mathematical Imagery, entitled "The Parallel Syndrome."

The Parallel Syndrome   by Miroslav Holub  (translated by Ewald Osers)

          Two parallels
          always meet
          when we draw them by our own hand.

          The question is only
          whether in front of us
          or behind us.

          Whether that train in the distance
          is coming
          or going.

The collection named above, in which Holub's poem appears, is available here.
This link leads to results of a blog search for previously posted poems by Holub..

One Idea May Hide Another . . .

     One of the excitements I find in both mathematics and poetry is the continuing discovery of new meaning.  A first reading discovers something but subsequent readings discover more and more.  A poem by Kenneth Koch (1925-2002), "One Train May Hide Another," opens with "In a poem, one line may hide another line" -- focusing also on the idea that one thought may obscure another.

     Koch's poem is one that I first met lots of years ago when I was working with middle school students in a poetry class at a newly established Children's Museum in Bloomsburg, Pennsylvania.  At the time, the poem excited me by bringing back memories of traveling through western Pennsylvania as a child when my parents' car often needed to obey flashing red lights and stop while a train crossed our highway.  And sometimes there were parallel sets of tracks and the possibility that two trains might be passing our intersection in opposite directions at the same time. 

     I offer below the opening lines of the poem and a link to the complete poem; I post it with the hope that you also will enjoy it -- and will reflect on the ways that (in mathematics and elsewhere) one idea may hide -- or lead to -- another.   

Geometry of a Neighborhood

     As we walk around, our views of our surroundings change;  lines that look parallel from one view appear to be converging from another . . . and so on.  The following poem by Massachusetts poet Martha Collins reflects on such view-changes:

House, Tree, Sky     by Martha Collins

If, when the pond is still
and nothing is moved
and the light is right.
you consider the angles
and make the proper approach,
you come to a bend
where a small white house
against a deep sky meets
the same white house against
the blue water:
stair rests on stair,
door opens on door,
tree grows out of tree.

Mother-daughter geometry -- in poetry . . .

     Last week (July 9) was the birthday of my mother -- and, although her body lies in a grave, her spirit continues to dance (and to both inform and confuse me).  Recently published in the Journal of Humanistic Mathematics (January 2019 issue) this poem by Jenny Patton -- a creative writing teacher at Ohio State University and a wellness coach -- has been provoking my memories. 

       Geometry of Night     by Jenny Patton

       In three-dimensional Euclidean space,
       lines in a plane that do not meet are parallel.

       My beautiful aunt loved to sleep, blogs
       my insomniac cousin about my mother
       who went to her parallel life every night.

       Those studying Playfair’s axiom note the
       constant distance between parallel lines. 

Reaching out . . .

Consider the geometry and community of  trees .  Can we learn from them?

          We plant two trees.

          Their trunks grow strong
          and straight--and parallel.
          Parallel lines don't meet.

          These trees, however--
          straight and tall and parallel--
          reach out with branches.

Sonnet for Bolyai -- and translations

     The Hungarian mathematician János Bolyai (1802 – 1860) was one of the discoverers of non-Euclidean geometry — an axiomatization  that differs from Euclid's geometry in its stipulations concerning parallel lines. This discovery of  an alternative view of space -- that also was logically consistent -- helped to free mathematicians to explore new ideas, and the consequences developed by Einstein and others have led to far-reaching results.
     Hungarian poet Mihály Babits (1883-1941) wrote a sonnet about Bolyai.  I learned of this sonnet and its English translation (by Paul Sohar and offered below) from Osmo Pekonen, a Finnish mathematician who is engaged in the project of collecting translations of Babits' sonnet into as many languages as possible.  (The original Hungarian version -- along with a Spanish translation -- is available here.) 

     Bolyai      by Mihály Babits              translation into English by Paul Sohar

     God had imprisoned our minds in space.
     Those puny things have remained prisoners.
     Thought, the hungry bird of prey fought the curse,
     but never breached its diamond bars' embrace.  

Blog history -- title, links for previous posts . . .

      My first posting in this blog was nearly eight years ago (on March 23, 2010).  If, at the time, I had anticipated its duration, I should have made a plan for organizing the posts.  But my ambitions were small.  During the time I was teaching mathematics at Bloomsburg University, I gathered poetry (and various historical materials) for assigned readings to enrich the students' course experiences. After my retirement, I had time to want to share these materials -- others were doing well at making historical material accessible to students but I thought poetry linked to mathematics needed to be shared more.  And so, with my posting of a poem I had written long ago celebrating the mathematical life of Emmy Noether, this blog began.  Particular topics featured often in postings include -- verse that celebrate women, verses that speak out against discrimination, verses that worry about climate change.   

You're invited to:
Scroll through the titles below, browsing to find items of interest
among the more-than-nine-hundred postings since March 2010
OR 
Click on any label -- a list is found in the right-hand column below the author profile 
OR
Enter term(s) in the SEARCH box -- and find all posts containing those terms.

 For example, here is a link to the results of a SEARCH using    math women 

And here is a link to a poem by Brian McCabe that celebrates math-woman Sophie Germain.
This link reaches a poem by Joan Cannon that laments her math-anxiety.
This poem expresses some of my own divided feelings.

                                       2017 Posts

Visual poetry -- schemes with squares

Thanks to math teacher Sara Katz (at Manhattan's Essex Street Academy) 

and the Journal of Humanistic Mathematics for today's poem.

Prime -- with rhythm and rhyme

     Earlier this year, an email from James D. Herren let me know about his recent e-book, Wit and Wonder, Poetry with Rhythm and Rhyme --  a collection developed to be enjoyed by readers from 5th grade onward.  Herren is an advocate of energetic rhyming verse, AND his collection has some mathy stuff -- including these two little poems.  Thanks, Dave! 

          Prime   by James D Herren

          Our love is prime –  
          Divisible by none
          But you and I,
          For you and I Are One.      

Math-Stat Awareness Month -- find a poem!

APRIL is Mathematics and Statistics Awareness Month
AND
National Poetry Month!

 Celebrate with a MATHY POEM, found here in this blog!  Scroll down!

If you are looking for mathy poems on a particular topic, the SEARCH box in the right-column may help you find them. For example, here is a link to posts found when I searched using the term "parallel."  And here are posts that include the term "angle."   To find a list of additional useful search terms, scroll down the right-hand column. 

For your browsing pleasure, here are the titles and dates of previous blog postings,

moving backward from the present.  Enjoy!

Mar 31  Math and poetry in film
Mar 28  Split this Rock, Freedom Plow Award, April 21
Mar 27  Math-themed poems at Poets.org
Mar 23  Remember Emmy Noether! 

December 2016 (and prior) -- titles, dates of posts

Here are the titles and dates of previous blog postings,

moving backward from the present.

For mathy poems related to a particular mathy topic -- such as women in math or climate or triangle or circle or teacher or . . . -- click on a selected title below or enter the desired term in the SEARCH box in the right-hand column.  For example, here is a link to a selection of poems found using the pair of search terms "women  equal."  For poems about calculus, follow this link.  To find a list of useful search terms, scroll down the right-hand column. 

     Dec 31  Happy New Year! -- Resolve to REWARD WOMEN!
     Dec 27  Celebrate Vera Rubin -- a WOMAN of science!
     Dec 26  Post-Christmas reflections from W. H. Auden
     Dec 19  Numbers for Christmas . . .
     Dec 15  Remembering Thomas Schelling (1921-2016)
     Dec 12  When one isn't enough ... words from a Cuban poet

When parallel lines meet, that is LOVE

Bernadette Turner teaches mathematics at Lincoln University in Missouri. And, via a long-ago email (lost for a while, and then found) she has offered this love poem enlivened by the terminology of geometry.

Parallel Lines Joined Forever    by Bernadette Turner

       We started out as just two parallel lines
       in the plane of life.
       I noticed your good points from afar,
       but always kept same distance.
       I assumed that you had not noticed me at all.  

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  

Math and Poetry and Climate

Canadian poet Madhur Anand is also an Environmental Scientist; her love of nature and concerns for preserving a habitable climate pervade her work -- and she also scatters throughout it some mathematics.  You can imagine my delight when I found in her new collection (A New Index for Predicting Catastrophes) a poem (included below) that features the identity matrix.  Read on!

No Two Things Can Be More Equal    by Madhur Anand

In undergrad I learned about the identity 
matrix. Ones on the main diagonal and zeros 
elsewhere. Anything multiplied by it is itself. 

Celebrating Ada Lovelace

Recently I have purchased the anthology, Raising Lilly Ledbetter:  Women Poets Occupying the Workplace (edited by Caroline Wright, M.L. Lyons & Eugenia Toledo, Lost Horse Press, 2015), and have found in it dozens of wonderful poems, including several that celebrate women of science.  Below I offer a poem by New York poet Jo Pitkin that honors Ada Lovelace (1815-1852).  

Bird, Moon, Engine     by Jo Pitkin

Like a fence or a wall to keep me from harm,
tutors circled me with logic, facts, theorems.
But I hid the weeds growing wild in my mind.

By age five, I could plot the arc of a rainbow.
I could explain perpendicular and parallel.
In my mind, I heard the wind in wild weeds. 

Balancing Opposites -- Tagore's Epigrams

Many important mathematical ideas occur as pairs of opposites:
         -2 and +2 (additive inverses), 5 and 1/5 (multiplicative inverses),  
         bounded and unbounded, rational and irrational, 
         convergent and divergent, finite and infinite
Some other familiar mathematical notions occur often in contrasting pairs but are not fully opposites:
         horizontal and vertical, positive and negative, 
         open and closed, perpendicular and parallel

Recently I have returned to reading work by Rabindranath Tagore (1861-1931; Bengal, India;  winner of the 1913 Nobel Prize in Literature) and I enjoy reflecting on contrasts posed by this reflective poet in a series of "Epigrams":

Epigrams      by Rabindranath Tagore

I will close my door to shut out all possible errors.
"But how am I to enter in?" cried Truth.  

Geometry of Love

     A couple of weeks ago my "Google Alert" linked me to a posting of a science poem concerning "the geometry of love."  The posting -- at The Finch and Pea -- is a poem that is both elegant and precise (and one that has been included in the anthology, Strange Attractors:  Poems of Love and Mathematics, that Sarah Glaz and I collected and edited several years ago).  Here it is:

The Definition of Love     by Andrew Marvell (England, 1621-1678)

My love is of a birth as rare
As ‘tis for object strange and high;
It was begotten by Despair
Upon Impossibility.  

Can you SEE the monument?

Links to non-intersecting celebrations of April
as National Poetry Month      and      Mathematics Awareness Month

are available here and here.

Recently I revisited my copy of Elizabeth Bishop:  The Compete Poems, 1927-1979 (FSG, 1999) and turned to "The Monument" -- a poem mathematically interesting for its geometry.  Here are the opening lines; the complete text and many other Bishop poems are available online here:

from  The Monument     by Elizabeth Bishop  (1911-1979)

     Now can you see the monument? It is of wood
     built somewhat like a box. No. Built
     like several boxes in descending sizes
     one above the other.
     Each is turned half-way round so that
     its corners point toward the sides
     of the one below and the angles alternate.  

Homage to Euclid

In my preceding post (20 March 2014) Katharine Merow's poem tells of the new geometries 

developed with variations of Euclid's Parallel Postulate.  

Martin Dickinson's poem, on the other hand, tells of richness within Euclid's geometry.

Poet and attorney Martin Dickinson is with the Environmental Law Institute and is a long term activist. The Nora School Poetry Series has scheduled both of us (along with Michele Wolf) to be part of a reading next month on April 24, 2014 .  It is my additional good fortune that conversations with Dickinson have included his sharing with me this mathy poem:

     Homage to Euclid       by Martin Dickinson

     What points are these,
     visible to us, yet revealing something invisible—
     invisible, yet real?