Sunday, January 31, 2016

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.

Wednesday, January 27, 2016

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. 

Monday, January 25, 2016

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,    

Saturday, January 23, 2016

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?  

Thursday, January 21, 2016

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

Wednesday, January 20, 2016

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!

Sunday, January 17, 2016

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? 

Tuesday, January 12, 2016

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! 

Friday, January 8, 2016

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 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


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.   

Tuesday, January 5, 2016

Counting those who grieve . . .

Each day's email brings me a Poem-a-Day from 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  

Saturday, January 2, 2016

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?