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  

Alphamath - poetry built on 4, 8

Since the late 1960s Toronto poet Victor Coleman has been energetically committed to innovated poetic practices.  A fine introduction to this poet is offered by Alex Porco in this linked review of Coleman's recent book, ivH: An Alphamath Serial (Book Thug, 2010).
          

          ivH: An Alphamath Serial is a book-length poem composed in the tradition 

of such precursors as Pythagoras, who taught that Number was the essence of all things; 

Plato, who argued that geometry was the foundation of all knowledge; 

Colorful mathematics for your smartphone

     "Bhaskara II (1114-1185) was an Indian mathematician and astronomer. He composed the Siddhanta Siromani, a treatise in four parts -- Lilavati (basics), Bijaganita (algebra), Grahaganita (planetary motion) and Goladhyaya (spheres)."
     This quotation comes from an early page of a new (2015) graphic e-book entitled The Illustrated Lilavati -- the text is based on a 1816 John Taylor translation, edited and illustrated for lilboox by Somdip Datta and available for download on smartphones and other devices.  Lilavati (named for the daughter of Bhaskara) was written in 1150 and was a standard textbook for arithmetic in India for many years.
     This e-book contains 25 illustrated problems (and solutions); here is the first:

This blog (then and now) and Pascal

     When I began this blog in 2010, I imagined up to 100 postings -- I saw it as a way to share math-related poetry that I had written and gathered during my years of teaching.  Now, as I prepare my 748th post, I am thinking about how I can organize my posts to make them findable and useful to the reader who visits and browses herein.

One thing that I have recently done is to update the blog's searchability -- 
in the right column you will find a search box.  

If you enter a term like "math" into the box, the search finds most of the posts in the entire blog and is thus not very helpful -- but you might try the term "triangle" and you would find about 20 relevant posts; one of them (from October 13, 2010) has the title "Varieties of triangles -- by Guillevic" and is the most-visited entry herein.  If you are, like me, someone who looks for math publicity and opportunities for girls, you may choose to enter "girl" in the search box.  This search, too, will lead to about 20 postings. 

Which hat? (from Slovenia)

     For a long time I have highly valued the work of Eastern European poets -- including Wislawa Szymborska, Miroslav Holub, Nichita Stanescu, Nina Cassian -- and have been pleased to find mathematical imagery in their work.  Early in November I had the privilege of attending a reading at the Goethe-Institut Washington that featured Slovenian poet Aleš Šteger -- born in 1973, winner of many awards, and described as the most translated Slovenian author of his generation.  A fun event -- from which I give you one of his slightly-mathematical offerings.

     Hat     by   Aleš Šteger (trans. Brian Henry)

     Who lives under the hat?
     Under the hat, which are three?
     Three hats. 

Are we speaking of "mathematics" or "poetry"?

     This week started with the excitement of an email message from Evelyn Lamb with a link to her Scientific American blog where she created a fun-to-take online poetry-math quiz based on an idea of mine (first published in 1992):

Can you tell the difference between mathematics and poetry?

Here’s a link to a SCIENTIFIC AMERICAN quiz to help you decide?

And a couple of centuries ago there was William Wordsworth -- who also contemplated both poetry and mathematics:

               On poetry and geometric truth
               and their high privilege of lasting life,
               From all internal injury exempt,
               I mused; upon these chiefly:  and at length,
               My senses yielding to the sultry air,
               Sleep seized me, and I passed into a dream.

William Wordsworth (1770-1850)

The Prelude, Book 5

Sustainability needs the arts AND mathematics . . .

The following poem is by Erica Jolly -- an Australian poet and retired teacher who is working hard to have the arts and the sciences integrated in Australian schools curricula.  “For too long, since the 1950s, we have witnessed serious losses across disciplines as science and mathematics have been deliberately separated from the arts and humanities,” Ms Jolly says.

"What has sustainability got to do with mathematics?"    by Erica Jolly

An exclamation attacking interdisciplinary themes in the national curriculum 

by Christopher Pyne on Q & A, 28 October 2013.

Does he not know or care
humankind must measure? 

Thanksgiving, 2015

Thinking toward Thanksgiving Day tomorrow, I am grateful for  --

 in addition to my children and grandchildren who will gather --

 all of the mathematic and poetic voices that help me see our world.
 Happy Thanksgiving wishes for all who read here!

Quoting Isaac Newton . . . . a "found" poem

     I do not know what
     I may appear to the world;
     but to myself I seem to have been
     only like a boy playing on the seashore,
     and diverting myself now and then
     finding a smoother pebble
     or a prettier shell than ordinary,
     whilst the great ocean of truth
     lay all undiscovered before me.

   -Isaac Newton, philosopher and mathematician (1642-1727)

Axiom: A Mathematics of Poetry

Today in a Facebook posting by Susanne Pumpluen

 I learned of Discov-her, an online journal 

featuring stories about women in Science. 

* * *

     The following poetry offering is by Richard Smyth who has written a parody of an introduction to the mathematics of logic (specifically Laws of Form by G Spencer Brown*, Julian Press, 1972).  Smyth founded Anabiosis Press which offers the poetry journal Albatross and which has now evolved into Anabiosis Online.  
     I invite you to enjoy this play of words and ideas:

AXIOM: A MATHEMATICS OF POETRY     by Richard Smyth

It shall be taken as given the idea of infinition. The idea of infinition stands in direct opposition to the idea of definition.

Definition
     Infinition is the act of making indefinite or unclear. That is to say, while some uses of language attempt to clarify, others attempt to obfuscate.

Construction
     Make a poem.  

Encouragement from fathers, a second view

     Despite the importance of fathers' encouragement (as noted in my post on 13 November), some women oppose their fathers' views.  Recently I have been enjoying Rachel Swaby's Headstrong: 52 Women Who Changed Science and the World  (Broadway Books, 2015) and yesterday my reading focused on her bios of Maria Agnesi (1718-1799) and Ada Lovelace (1815-1852) and the roles their fathers played in their lives.  Agnesi was a child prodigy who wished to be a nun but followed her father's wish that she research in mathematics until his death, when she was thirty-four; she devoted the rest of her life to serving the poor.  The education of Ada Lovelace was directed by her mother who did not see her father, the poet Lord Byron, as a solid foundation.  
     Poetic expression by a daughter somewhat resistant to her father's wishes comes from our youngest-ever US Poet Laureate Rita Dove in her poem, "Flash Cards": 

Encouragement from fathers

     It was my observation as a professor in a mostly-male mathematics department that the men who joined me in supporting opportunities for women were fathers of daughters.  They had come to see the world from a new perspective -- and saw that it needed changing.  Somewhat along these lines was a recent Washington POST article that told of recent research findings about socially responsible behavior from CEO's with daughters.
      With these thoughts in mind I started counting words . . . wanting to form a poem:

Limericks for Hedy Lamarr

     When seeking to draft a poem quickly, it is useful to have some sort of pattern to follow -- a pattern helping to dictate word choice.  This morning, upon discovering Google's online celebration of the 101st birthday of inventor and actress Hedy Lamarr, I have wanted to join the commemoration with a poem.  A verse pattern rather often used by hasty math writers is the limerick (see links below) -- and I have today constructed this pair of limericks to praise Lamarr.

     May a beautiful actress present
     Skills beyond stage and screen content?
          Yes!  Hedy Lamarr
          Excelled as a star,
     And had also talent to invent!