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.

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. 

Artificial Intelligence in the Library . . .

     Libraries are wonderful places and library book sales are temptations impossible to resist -- and so, during a recent trip to Boston and exploration of the historic public library buildings on Boylston Street, I purchased a copy of Living Proof  (Florida International University Press, 1985) by Edmund Skellings (1932-2012).  Born in Boston and a poet laureate of Florida, Skellings was a pioneer in the application of computers to the arts and humanities.  The word "proof" in his title was enough to make me pick up the book and I have relished the opportunity to turn up memories of a long ago graduate course in AI while reading this poem:

Artificial Intelligence     by Edmund Skellings

Euclid rolled over in his bones
When Newell & Simon instructed
Their machine to look for new proof
For bisecting the ordinary triangle.   

Galileo in Florence

Poetry found in the words of Galileo Galilei (1564-1642):

"Philosophy is written in this grand book,
the universe, which stands continually
open to our gaze. 

But the book cannot be understood unless one first 
learns to comprehend the language and read the letters
in which it is composed.

It is written in the language of mathematics,

The Girl Who Loved Triangles

     I found this poem by Michigan poet Jackie Bartley when I was browsing old issues of albatross (edited by Richard Smyth) and she has give me permission to post it here.  Like Guillevic (see, for example, this earlier post), Bartley has found personalities in geometric figures.

To the Girl Who Loved Triangles     by Jackie Bartley

          Triangulation:  Technique for establishing the distance between two points
                                      using a triangle with at least one side of known length.

One girl in a friend's preschool class
loves the triangle.  Tanya's favorite shape,
the children call it.  Simple, three sided, at least

one slope inherent, slip-slide down
in the playground of mind.  Tension and its
release.  Sure balance, solid as the pyramids.  The 

Pound on poetry and mathematics

HERE at PoetryFoundation.org we find an article by Carl Sandburg (1878-1967), published in POETRY Magazine in 1916, in which Sandburg offers highest praise to poet Ezra Pound (1885-1972). Sandburg includes this quote from a 1910 essay by Pound that connects poetry and mathematics.

"Poetry is a sort of inspired mathematics, which gives us equations, 

not for abstract figures, triangles, spheres and the like, but equations 

for the human emotions.  If one have a mind which inclines to magic

rather than science,  one will prefer to speak of these equations 

as spells or incantations; it sounds more arcane, mysterious, recondite."

The complete article is available here.

And, in a footnote* to the poem "In a Station of the Metro" -- found in my Norton Anthology of Modern Poetry we find a bit more of Pound's mathematical thinking. 

Remembering Nina Cassian

Exiled Romanian poet Nina Cassian (1924-2014) died last week in Manhattan.  Cassian was an outspoken poet whom I admired for her political views; she also was connected to mathematics -- in her subject matter and her friends.  (See, for example, this posting from January 31, 2011.)

       Equality     by Nina Cassian

       If I dress up like a peacock,
       you dress like a kangaroo.
       If I make myself into a triangle,
       you acquire the shape of an egg.
       If I were to climb on water,
       you'd climb on mirrors.

       All our gestures
       Belong to the solar system.

"Equality" is in Cheerleaders for a Funeral (Forrest Books, 1992), translated by the author and Brenda Walker.

Enough for everyone -- Russell Libby

Are you looking for a poem on a particular math topic?  One search strategy is to go to the Poetry Foundation website (another is to click on the green SEARCH BOX in the right column of this blog) and enter your math term into the search box; if, for example, you enter "geometry" one of the poems you find will be this one by Russell Libby (1956  -2012).  Both poet and organic farmer, Libby believed in sustainability:  all it takes is one well-cared-for seed to grow and spread.  Here is his "Applied Geometry." 

     Applied Geometry     by Russell Libby

     Applied geometry,   

     measuring the height   

     of a pine from   

     like triangles,   

Is Algebra Necessary?

     Anticipating my interest, several friends sent me links to a late-July opinion piece in The New York Times entitled "Is Algebra Necessary?" (written by an emeritus political science professor, Andrew Hacker).   I more-or-less agree with Hacker that algebra is not necessary in most daily lives or places of employment.  In fact, years ago I developed a non-algebra text, Mathematics in Daily Life,  for a course designed to satisfy a math-literacy requirement at Bloomsburg University.  On the other hand, my own fluency in the language of algebra opened doors to calculus and to physics and so many other rooms of knowledge that I have loved.
     Expressing algebraic issues in verse, we have this thoughtful poem by Jeannine Hall Gailey, Poet Laureate of Redmond, Washington (home of Microsoft). 

Spanish favorites

One of my favorite DC-area poet-people is Yvette Neisser Moreno -- who, besides giving us her own work, is active in translation of  Spanish-language poetry into English, most recently (with Patricia Bejarano Fisher) a Spanish and English edition of Venezuelan poet Maria Teresa Ogliastri’s South Pole/Polo Sur  (Settlement House, 2011).  Although I have not found any mathematical poems by Moreno, I learned from an interview that the Chilean Nobelist Pablo Neruda (1904-1973) is her favorite poet and I therefore present here the geometrically vivid opening opening stanza of Part XI of Neruda's well-known long poem, The Heights of Macchu Pichu: A Bilingual Edition (The Noonday Press, 1966). 

The hypotenuse of an isosceles triangle

Detroit poet, Philip Levine, has been selected as the new Poet Laureate of the United States. Selected by the librarian of Congress (James Billington), Levine follows poet W. S. Merwin in the honored position.  A Poet Laureate is responsible merely for giving readings in October and May but some laureates also use the position to proselytize for poetry.   Here, from Levine's early collection, What Work Is (Knopf, 1992), is a poem that looks back on a math-art moment in a middle-school classroom.

Found in Flatland

Over the years I have shared with friends and students my copy of Edwin Abbott's Flatland (first published in England in 1884) and, alas, not all of these other readers have matched my level of excitement with the small volume.  Even though the book's Victorian attitudes are mostly at odds with my own views, still the tiny book opened me to possibilities of new ways of seeing. Since observing the Flatlanders stuck in two dimensions from my advantageous three-dimensional position, I have wondered how I can now make the leap from three to four or more dimensions.

Mathematics and race

Sherman Alexie is a Spokane / Coeur d’Alene Indian from Wellpinit, Washington. Besides several collections of poetry, Alexie has published novels and short-stories; he wrote the screen-play for the 1998 film, Smoke Signals. Here, in verse, he deals with the mathematics of racial identity:

Varieties of triangles -- by Guillevic

My introduction to French poet Guillevic (1909-97) came from UK poet Tim Love who found three of his triangle poems translated into Italian.  Jacqueline Lapidus translated them for me from French into English, after which I also found Guillevic's collection Geometries (Englished by Richard Sieburth, Ugly Duckling Presse, 2010) -- with its circles, ellipses, parallels, and so on.  And so, beyond these three, there will be more to enjoy later.  

A poem of calculus (of ants on a worm)

Philip Wexler plays with the terminology of calculus in this poem:

     The Calculus of Ants on a Worm

     Swarming tiny
     bodies nibble
     away, no limits,

Margaret Cavendish (1623-73) -- The Circle of the Brain cannot be Squared

Margaret Cavendish (1623-73) was a writer who published under her own name at a time when most women published anonymously.  Her writing addressed a number of topics, including gender equity and scientific method.