Poems with Fibonacci number patterns

In 21st century poetry, there are a variety of non-rhyming forms--and several of them have derived from the Fibonacci numbers.*  The Danish poet, Inger Christensen (1935-2009), wrote a book-length poem, alphabet (New Directions, 2000) in which the numbers of lines in stanzas followed the sequence of Fibonacci numbers.  "Fibonacci," shown below, by Judith Baumel is a shorter example of this form.

A Numerical Poem (Fibonacci)

Consider the following poem involving the Fibonacci numbers:
 

        1/89 = .0        +

                  .01        +

                  .001        +

                  .0002        +

                  .00003        +             

                  .000005        +

                  .0000008        +

                  .00000013        +

                  .000000021        +

                  .0000000034        +

                  .00000000055        +

                  .000000000089        +

                  .0000000000144        +

                  .  ...

A special Fibonacci poem

     A recent email from Marian Christie -- a nominally retired mathematics teacher from Aberdeenshire  -- alerted me to her very special sort of Fibonacci poem, one in which the number of letters-per-line follows the Fibonacci numbers AND the length of each word is a Fibonacci number AND the poem speaks about the objects counted by these Fibonacci numbers.

Pathways      by Marian Christie
–
O
I
am
not
going
anywhere
unaccompanied
by life’s patterns: a whorl
in a pinecone, branches on oak or elm trees, 
the petal count of a daisy, the helix at the heart of a chrysanthemum,
the shell of a nautilus swimming in the ocean. A sequence hides in the shape of
                                                                             probabilities, and in my own DNA. 

Poet's Note: In this poem the number of letters per line is determined by the Fibonacci sequence: the first line has zero letters while the last line, representing the twelfth number in the sequence, contains 89 letters. In addition, the letters of each word add up to a Fibonacci number.  

Christie's poem was first published on the UK-based website IndependentVariable.

The Fib -- a form that gathers strength

The "Fib" is a poetry form in which the numbers of syllables per line follow the pattern of the Fibonacci numbers.  (See also April 19 and April 29 postings.)   The sequence of Fibonacci numbers starts with 0 and 1 and then each successive Fibonacci number is the sum of the two preceding.  Thus, the non-zero members of the sequence are:
          1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
Poet Athena Kildegaard's collection Red Momentum (Red Dragonfly Press, 2006 ) consists entirely of Fibonacci poems.  The following samples from Kildegaard's collection illustrate the way that increasing line lengths can build to dramatic effect. From a simple start, complexity grows.

Happy Fibonacci Day!

        Today, November 23 is Fibonacci Day . . . How are you celebrating?  Twitter poet Brian Bilston (@Brian_Bilston) has posted a Fibonacci poem -- with words-per-line counted by the Fibonacci numbers.  Here are its opening lines:

       I
       wrote
       a poem
       in a tweet
       but then each line grew
       to the word sum of the previous two
       until . . .

Use of the Fibonacci numbers in poetry has gotten frequent mention in this blog; here is a link to the results of a blog SEARCH using the term Fibonacci.  And find the rest of Brian's poem in this posting from August 31, 2020 -- or by browsing here on Twitter.

Recursion

A mathematician may face a dilemma over the meaning of an ordinary term -- for words like "group" and "identity" and "random" (to name a few) have precise mathematical definitions that differ from their common meanings. Canadian poet Peter Norman's title, "Recursion," however, uses the term as it is used mathematically.  While a definition of "recursion" is widely available in mathematics texts, it was missing in my several English dictionaries -- and I found it only in the OED (though, even there,  noted as now rare or Obs.) : "a backward movement, return."   The term "return" indicates previous forward motion. In mathematical recursion (illustrated below by the Fibonacci sequence) as in Norman's poem, going backward is possible only because forward motion is known. (Interested readers will find an introduction to mathematical recursion following the poem.)

     Recursion    by Peter Norman

     I fall awake alone. Outside,
     nocturnal rain ascends.  

Fibs in NZ -- and climate change

     A few days ago, on August 21, it was Poet's Day in New Zealand and the blog sciencelens.com featured a math-poetry theme; that posting mentions the anthology, Strange Attractors:  Poems of Love and Mathematics (for which Sarah Glaz and I are co-editors) and offers several Fibs, poems whose syllable-counts follow the first six non-zero Fibonacci numbers (1, 1, 2, 3, 5, 8, . . .., with each succeeding number the sum of the two preceding). 

Writing -- a Path toward Knowing

     Advice for my grandchildren -- in the form of a Fib.  (Wish I had remembered to give it on November 23 -- which is Fibonacci day. ) 

 

    1            When

    1            I

    2            want to

    3            understand

    5            something difficult

    8            I grab my pen, write about it.

     I'm not sure when I made the discovery but by the time I was in graduate school  I knew that my learning pattern involved my fingers and my pen.  I copied definitions into a notebook, sometimes trying to rephrase them in my own words.  I elaborated the proofs of theorems . . . my fingers helped me remember.

November 23 is celebrated as Fibonacci day because when the date is written in the mm/dd format (11/23), the digits in the date form a Fibonacci sequence: 1,1,2,3. A Fibonacci sequence is a series of numbers where a number is the sum of the two numbers before it.  A Fib is a tiny poem whose lines have as syllable-counts the first 6 Fibonacci numbers.  

For more Fibonacci-related poems, follow this link. 

Nature's Examples of Fibonacci Numbers

     Recently I have been reexamining some of the treasures that have been on my bookshelves for a while.  One of these is Discovering Patterns in Mathematics and Poetry by Marcia Birken and Anne C. Coon (Rodopi B. V., 2008).  And, on page 60 of that collection,  I find "Fibonacci Time Lines" by Kansas poet Michael L.Johnson --  the poem is a lovely weave of the Fibonacci numbers with objects they count  (and was originally published in The Unicorn Captured (Cottonwood Review Press, 1980)) and, with the poet's permission, is offered below.

     Fibonacci Time Lines    by Michael Johnson

     cat's
     claw's
     curl, pine
     cone's swirl, goat's
     horn's turn, nautilus'
     shell's homing out, pineapple's whorl,
     sneezewort's branchings, hair's twist, parrot's beak's growth, 
            elephant's
     tusk's curve, monkey's tail's spiral, cochlea's whirl of sound, 
           Vitruvius' analogies, 
     Parthenon's geometry, logarithms' golden sections, time's way 
            through form, mind's acceleration on its helical vector 
            to death . . .

Here is a link to a host of poems linked to the Fibonacci numbers and found in earlier postings in this blog.

Looking back . . . titles, links to previous posts

      For your browsing pleasure,here are titles and links to previous blog postings.  Below are listed linked-titles of posts from 2018 and up-to now in 2019 and here is a link to a list of titles and links for posts prior to 2018.  

•       March 13   An Interview of/by a Mathy Poet
•       March 11   Celebrate Pi-Day on 3.14
•       March  6    Celebrate Math-Women with Poems!
•       March  4    Math in 17 Syllables

February 2019: 

• Solving for X, Searching for LIFE
• Stories of Black Mathematicians (event postponed)
• All Numbers are Interesting . . .
• George Washington, cherry tree, lifespan . . .
• Musical sounds of math words -- in a CENTO
• If 2017 was a poem title . . .
• Mathematics and Valentine's Day
• Speed flunking math . . . NO, NO!
• Quantum Lyrics -- Poems

Celebrate math students -- a Fibonacci poem!

     South Dakota mathematician Dan May teaches mathematics at Black Hills State University where he also leads workshops for middle school teachers, explores musicology and the connections between poetry and discrete mathematics. He has been involved in math-poetry activities at Bridges Math-Arts conferences but, more importantly, he has been involved with BEAM (Bridge to Enter Advanced Mathematics), a program offering varied academic assistance to underserved students, including a summer residential program. The following Fibonacci poem celebrates that adventure.

BEAM: A Fibonacci Poem     by Dan May

Now
you 
are home — 
Brooklyn, Queens, 
the Bronx, your boroughs. 
Only yesterday still at camp, 
learning knots and graphs, writing proofs on infinity. 
I taught you the one hundred and sixty-eight automorphisms of the Fano plane. 
You wear hijabs, or Jordans, or both. Diverse faces 
display the doubts of twelve-year-olds. 
But each of you, when 
you get it — 
your face 
lights 
Up.

Author’s Note: The poem’s syllable line count follows the 

Fibonacci sequence numbers 1, 1, 2, 3, 5, 8, 13, 21 forward and backward.  

This poem and several others of Dan May's math-linked poems may be found here.

Number Patterns in Nature

     Naval Academy engineering professor and math-poetry fan Gregory Coxson has recently introduced me to poetry by Mattie Quesenberry Smith at VMI (for a bio of Smith, go to this page, scroll down, click on BIO) -- she and I have connected and she has shared with me several of her mathy poems; here is one about the Fibonacci numbers -- a number pattern found in nature:  

     Fibonacci Found It       by Mattie Quesenberry Smith

        It is spring on House Mountain,
          And I am wondering how
          Fibonacci found it
          And believed that it matters,
          That sequence of numbers
          Hinging on what precedes them,   
          Running this springtime show.
          Soon spring will be sanguine,
          Shouting from steep shadows,
          And the eight-petaled bloodroot,
          A robust and pure lion
          Rooted in his bloody rhizome,
          Is a rare know-it-all.
          A leaf encircles his stem.
          Its strange, veined palm
          Shields him from blood’s loss.

 ”Fibonacci Found It” was first published in Thirty Days: The Best of the Tupelo Press 30/30 Project’s First Year,” edited by Marie Gauthier, Tupelo Press, 2015. Reprint rights are retained by author.

Discovery Tool -- Following a Pattern

     When I pick up a pen to write on a particular subject, often it is useful me to try to follow a pattern for rhymes or syllable-counts -- for the effort to conform to a pattern challenges me to think about my topic in new ways.  In the history of poetry, rhyme-choices were frequent--yielding sonnets, villanelles and a variety of other forms.  

     In recent years, online and printed versions of poems have become very accessible and the principle, "Rhymes help us remember" has become less of a focus in poetry.  One of the popular connections between math and poetry has been the use of Fibonacci numbers to choose syllable counts;  especially  popular has been the FIB, a six-line stanza in which the syllable-counts are 1, 1, 2, 3, 5, and 8 -- the first six Fibonacci numbers.  (Inventor of the FIB was Greg Pincus, and lots of information is provided here in this 2010 blog posting, Poems with Fibonacci number patterns.)  

In the Tuscan sun

View
the
statue
in Pisa
of Fibonacci,
mathematician in the sun.  

Twelveness -- a Fibonacci poem from G4G

     Science writer, philosopher, and skeptic Martin Gardner (1914-2010) is perhaps best known for his long-running Scientific American column, "Mathematical Games."  His life and work are celebrated by G4G conferences ("Gatherings for Gardner") held in even-numbered years in Atlanta.  Here fans gather and present fun-mathematics to each other.
     A several-time participant in G4G is Kate Jones of Kadon Enterprises, an organization devoted to the development and distribution of Game Puzzles.  Below in a Fibonacci poem created for the 2016 G4G Jones tells the history of her game-puzzle enterprise.

Many Fibonacci poems use the Fibonacci number sequence 

to determine the numbers of syllables in successive lines of a poem.  

In the following poem, it is the numbers of words that are counted.
 A pentomino is a plane geometric figure formed by joining five equal squares edge to edge.  
There are twelve differently-shaped pentominos; this number gives the title of Jones's poem.

TWELVENESS  by Kate Jones

  1    Martin
  1    Gardner
  2    Long ago
  3    Wrote about pentominoes,
  5    Brainchild of young Solomon Golomb,
  8    The coolest recmath set in all the world.   

Shaping a Poem with Fibonacci numbers

      One of my favorite websites to visit is this varied and thoughtful "Poetry and Mathematics"  collection of postings by Marian Christie.

     Throughout history, people who write poems have often been aided by constraints.  When we sit down to write, writing the words that first occur to us -- then shaping the word into extended meanings but following a pattern of rhythm or rhyme or word-count . . . or . . .  .  For many poets the sonnet, for example, has been a poetic structure that shapes thoughts into special arrangements of words.

     In long-ago days, when print and screen versions of poems were not easily available, rhyme schemes were an important aid -- helping one's memory to keep a poem in one's head.  Now, aided by widely available print and online visibility, poetry has moved into new forms -- including a variety of visual arrangements.  

Mathematics and poetry -- are the same ! ! !

Last week the Art Works Blog posted an interview with mathematician, poet, and translator, Enriqueta Carrington.  You will want to follow the link and read the whole thing.  Here is a paragraph:

quoting Enriqueta Carrington:

Mathematics and poetry are the same thing,
 or one is a translation of the other.

Well, perhaps that is an overstatement; 
but both math and poetry are about beautiful patterns, 
about creating, gazing at, and sharing them, 

and about appreciating those created by others.

It is not necessary to be a great mathematician or a great poet 
to enjoy this beauty, as I can tell you from my own experience.

Several years ago, at a time near the beginning of this poetry-math blog, in the posting for April 8, 2010, is a pantoum by Carrington.  And here is another of hers, this time a Fibonacci poem -- whose lines increase in word-count that matches the first eight Fibonacci numbers:  1, 1, 2, 3, 5, 8, 13, 21.

Another Fibonacci poem . . .

     Through many years of the history of poetry, the sonnet has been a treasured form -- as poets strive carefully to match the iambic pentameter rhythm and some pattern of rhyme, this concentrated thinking leads to careful word choices and memorable poems.  (Here is a link to a mathy sonnet by a math teacher's son, John Updike.)
     Modern poetry has many "free verse" poems that follow no particular form AND ALSO a variety of new forms.  One particularly popular format (appearing often in this blog) is to count syllables-per-line using the Fibonacci numbers   Here an interesting example by poet Marian Christie which describes increasing complexities of crocheting using Fibonacci syllable-counts.

"Crochet" -- a FIB by Marian Christie

 Christie's poem was first published in here in Issue 36 of The Fib Review.

Speaking in Fibs . . .

     Syllable-count patterns often are used in poems--helping to give a rhythmic tempo to the words.  As I mention often, syllable counts -- and other word-patterns -- help me to discover new and special meanings to convey. When I start to write, my thoughts are scattered and need to be gathered and focused -- and a poetic form helps this to happen.  The sonnet and the villanelle have long been valued examples of poetry patterns.  More recent -- and more simple -- is the Fib.  Introduced by poet Gregory Pincus back in 2006, the Fib is a six-line poem whose syllables are counted by the first six Fibonacci numbers:  1, 1, 2, 3, 5, 8. (Each succeeding Fibonacci number is the sum of the two that precede it.)

     Since 2006, a journal aptly named The Fib Review has offered (available at this website) more than 40 issues of poems, all of whose lines have syllable-counts that are  Fibonacci numbers.  Here is a portion of one of the poems -- by Washington-based poet Sterling Warner --  (the complete poem is found here).

Here is a link to another blog posting that features poetry from The Fib Review.

And lots more FIBS may be found here.

A small Fib

My dilemma

   I've
   lost
   the art
   of careful
   thought, asea in floods
   of  trivial  information.               by JoAnne Growney