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.

Words of Ada Lovelace

These poetic words of Ada Lovelace (1815-1852) -- concerning translation of mathematical principles into practical forms -- I found here:

Those who view mathematical science,
not merely as a vast body
of abstract and immutable truths,
whose intrinsic beauty, symmetry and logical completeness,
when regarded in their connexion together as a whole,
entitle them to a prominent place 
in the interest of all profound and logical minds,  

A Fractal Poem

    A fractal is an object that displays self-similarity -- roughly, this means that the parts have the same shape as the whole -- as in the following diagram which shows successive stages in the development of the "box fractal" (from Wolfram MathWorld). 

   
Michigan poet Jack Ridl and I share an alma mater (Pennsylvania's Westminster College) and we recently connected when I found mathematical ideas in the poems in his collection Broken Symmetry  (Wayne State University Press, 2006); from that collection, here is "Fractals" -- offering us a poetic version of self-similar structure:

       Fractals    by Jack Ridl

       On this autumn afternoon, the light  
       falls across the last sentence in a letter,
       just before the last movement of Brahms’ 
       Fourth Symphony, a recording made more 
       than 20 years ago, the time when we were  
       looking for a house to rehabilitate, maybe  

From order to chaos -- a sonnet

Fractals    by Diana Der-Hovanessian

                             Euclid alone has looked on beauty bare
                                                    --Edna St. Vincent Millay

Euclid alone began to formulate
the relation of circle, plane and sphere
in equations making it quite clear
that symmetry is what we celebrate. 

Symmetry in poetry

In Euclidean Geometry, objects retain their size and shape during rigid motions (also called symmetries); one of these is translation -- movement of an object from one place to another along a straight line path.  Here are a few lines by Alberta poet Alice Major that explore the paths of rhyme as a sound moves to and fro within a poem :

     Rhyme's tiles slide
               from line
     to line, a not-so-rigid motion --
     a knitted, shifting symmetry
               that matches 'tree' 

Symmetric stanza

Although the following stanza by mathematician-author Lewis Carroll first appears to be a merely melodramatic example of Victorian verse, a bit of scrutiny reveals its special symmetry.

     I often wondered when I cursed,
     Often feared where I would be—
     Wondered where she’d yield her love
     When I yield, so will she,
     I would her will be pitied!
     Cursed be love! She pitied me…

This 6 line stanza by Carroll (well-known for for his nonsense verse) reads the same both horizontally and vertically. 

One type of "mathematical" poetry

When I began (in the 1980s) collecting examples of "mathematical poetry," I sought lines of verse that included some mathematical terminology.  More recently, my view has expanded to include structual, visual, and algorithmic influcences from mathematics; however, the two samples from the work of William Blake (1757-1827), presented below, fit into that initial category -- selected as "mathematical" because of their vocabulary -- one speaks of "infinity," the other of "symmetry."  (Blake was an artist as well as poet and his volumes of poetry were illustrated with his prints.)  The following stanza is the opening quatrain for Blake's poem "Auguries of Innocence."