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Mathematics Merges with Verse.

I suppose all verse involves mathematics in the measure of the line and length of the stanza, but there are a few verse forms that were invented specifically from mathematical concepts.

Cadae was found in two forms. The word "cadae" is the alphabetical equivalent of the first five digits of Pi, 3.1415. (I never did understand Pi, how did I survive algebra?) But for you mathematicians, this may be a verse form you could have fun with. Both forms are similar in concept with the Fibonacci.

  • The Cadae #1 -I found this form at a site for teachers, the form is a way of introducing the numbers of Pi to children. This verse form uses the first 5 digits of Pi to determine the number of lines in a strophe and the numbers of syllables in the line.

    The elements of the Cadae #1 are:

    1. strophic, written in 5 strophes of fixed but varied length.

      S1 - 3 lines
      S2 - 1 line
      S3 - 4 lines
      S4 - 1 line
      S5 - 5 lines

    2. syllabic,

      S1 - 3 syllables per line
      S2 - 1 syllable in the line
      S3 - 4 syllables per line
      S4 - 1 syllable in the line
      S5 - 5 syllables per line

      Pi ∆∆∆∆∆  by Judi Van Gorder

      A circle
      and measured


      and diced into
      pie shaped pieces . . .
      divides into


      whole circumference
      the answer is Pi . . .
      pie placed side by side
      joined at the bottom
      creates cadae crown.

  • Cadae #2 is a Western experimental movement to merge math and verse. This was found at Wikipedia. It is much more complicated than the children's version above. This form counts strophes, lines and syllables. There is even the option for the truly mathematically inclined to count the letters of the words in sequential order with the numbers or digits of Pi. Pi = 3.1 41592653589793238462643383279502884197 to infinity..

    The elements of the Cadae #2 are:

    1. Strophic, 5 strophes, each containing the number of lines in sync with the first 5 digits of Pi. S1=3 line, S2=1 line, S3=4 lines, S4=1 line, S5=5 lines. 14 lines altogether.
    2. Syllabic, 3-1-4-1-5-9-2-6-5-3-5-8-9-7 syllables per line.
    3. Unrhymed.
    4. Variable: For a Cadae on steroids, the poet could take this a step further and in addition to the strophe, line and syllable count, the number of letters in the words of the poem could also follow the sequential numbers of Pi.

      The following is a "pumped up" Cadae and employs all of the above features. This poem includes 40 words with the letters in sync with the first 40 digits of Pi=3.141592653589793238462643383279502884197. As long as the strophe, line, syllable and letter count are in sync with the digits of Pi, the word count could vary from poem to poem.

      Cadaeic Cadae by Rachel Hommel

      God – a gift
      swore mordantly
      to. .
      . . . reject daily, but,
      human toxicity resonates
      seditious men of war
      stealing love "aweigh"
      He abhors .
      Axis and Ego;
      fighting was an age-long righteous
      brawl & my previous exertion
      bred a chastened warrior.

Cadaeic Cadenza (Cadenza is Italian for cadence.) is named for a short story written in 1996 by Mathematician Mike Keith. It is said to be an example of "constrained writing". The number of letters in each word sequentially mimic the first 3825 digits of Pi. In terms of merging poetry with math, in this case "Pi", the poet need only follow the sequential digits of Pi either in word, syllable, or letter count or all of the above.

Found at Wikipedia: The parody of Poe's Raven written in Cadae Cadence the letters of the words in the sequence of Pi 3.1415 (author and title) etc.

Poe, E. Near a Raven

Midnights so dreary,
tired and weary,
Silently pondering volumes
extolling all by-now obsolete lore.
During my rather long nap -
the weirdest tap!
An ominous vibrating sound
disturbing my chamber's antedoor."
"I ignore"
    .--- Mike Keith, First stanza of Near a Raven                          


A Raven by Edgar Allen Poe

Once upon a midnight dreary,
while I pondered, weak and weary,
Over many a quaint and curious
volume of forgotten lore,
While I nodded, nearly napping,
suddenly there came a tapping,
As of some one gently rapping,
rapping at my chamber door."'
Tis some visitor," I muttered, "
tapping at my chamber door —
Only this, and nothing more."

Chronos is another mathematical verse form built around the root of Pi, this time Pi2 or Chronos = 9,8696. I found this verse form created by Bianca at Writing .com The elements of the Chronos are:

  1. a pentastich.
  2. syllabic, 9-8-6-9-6 syllables per line.

The Fib is the brainchild of American screenwriter, Gregory Pincus found in his blog at GottaBook in 2006. The Fib is his solution for the need to write Haiku with a few more syllables. Based on the Fibonacci concept of the sequential numbers 0-1-1-2-3-5-8, It is a hexastich with progressive syllable count and has become very popular on the internet. The elements of the Fib are:

  1. a hexastich, a poem in 6 lines
  2. syllabic, syllables 1-1-2-3-5-8

    Here are a couple of poems by Lucy Lu that demonstrate the Fib

    he is
    there watching
    on the other end.
    My heart quivers at such a thought.                                
    white or black,
    the one that catches
    the mouse is a good cat. Topnotch!

The Fibonacci, along the same lines as the Fib, the Fibonacci is a movement to write verse utilizing and named for a mathematical concept developed by the 12th-century Italian mathematician Leonardo Pisano Fibonacci. The Fibonacci numbers are 0,1,1,2,3,5,8,13, 21  and so on, adding the last 2 numbers to determine the next in line. The form appears to be first used by poets in the 20th century in America and Denmark. It is similar in concept with the Cadae. Unlike the Fib, it is the stanzaic, rather than syllable count, the stanzas progress to correspond with the numeric concept. The elements of the Fibonacci are:

  1. stanzaic, written in any number of stanzas in which the number of lines of each stanza increases corresponding with the Fibonacci concept as the poem progresses.
  2. rhyme and meter are written at the discretion of the poet.

    Together Forever by Judi Van Gorder

    Holding hands at sunset

    Dreams of yesterday
    lovers side by side.

    It all begins
    in love with love
    timeless touch.

    Dreams do not anticipate
    a hospital marathon
    palsied hands
    a shoulder leaning heavily
    a life on hold.

    Watching you sleep
    brought pleasure, felt safe.
    Now I'm left to wonder
    if you will wake
    stay with me one more day
    or will you release me
    from my vigil?
    Forever is a long time.

Fibonacci Spiral is an invented form by Georgia Luna Smith Faust also using the numbers of the Fibonacci numbers 0-1-1-2-3-5-8-13, syllables create a spiral image . The elements of the Fibonacci Spiral are:

  1. a poem in 25 lines with no stanza break.
  2. syllabic,  syllables per line 1-1-2-3-5-8-13-8-5-3-2-1-1-1-1-1-2-3-5-8-13-8-5-3-2-1-1
  3. L12, 1 syllable word must be at least 4 letters
  4. L13 is repeated as L14
  5. centered on the page


Pi-Archimedes is a simpler variation of the Cadae Verse. Named for the Greek mathematician Archimedes, (c. 287 BC – c. 212 BC) who defined Pi. In this verse, the first six digits of Pi are represented by 6 lines and word count per line. Pi = 3.14159 . . (My original source is lost to me and it was recently pointed out that I had incorrectly posted the sequential digits of Pi. I don't know if this was my error or an error from the original source. I have corrected the 6 numbers and the word count for each line to the correct sequence.)  The elements of the Pi-Archimedes verse are:

  1. a hexastich, a poem in 6 lines.
  2. measured by the number of words in each line 3-1-4-1-5-9 to match the numerical sequence of the first six digits of Pi.
  3. unrhymed.

    Pi by Judi Van Gorder

    Not my thing,
    Algebra is an enigma,
    that mucks up my brain.
    "You use math every day", they say.  I try.

The Piaku is an invented form that takes its syllable count from the Pi. Created by American Mike Rollins this form may have an infinite number of lines. Found at All Poetry in Lawrencelot’s Blog.  The elements of the Piaku are:

  1. Is written based on the number Pi = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 ...on to infinity… with each number representing a line. It is at the poet’s discretion how many lines the piece should include which could go into infinity. One could argue that the poem should begin with a single line followed by any number of quintains, but the original example poem is not broken into stanzas.(more choices for the poet)
  2. Syllabic, syllables per line pi=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 ...
  3. Unrhymed.

    (In the following poem I chose to write in quintains and use the first syllable count of 3 for the title.

    Complex Math by Judi Van Gorder

    the infinite
    number without end
    unequivocal revelation.

    one could spin into
    the farthest reaches
    of the mind
    and never come back.

Quaternion is a verse form named for the algebraic equations that were introduced by Irish mathematician Sir William Rowan Hamilton in 1843 which completely oversimplified and probably missing the point entirely are the multiplication of three dimensional imaginary units by four dimensional objects. Now don't expect me to explain that. The verse form is English in origin and found at Poetry Base. The only connection I see between the algebraic concept and the form is they both have a 3 by 4 concept. The form is written in three quatrains with a rhyme scheme that ends with a combination of the rhyme of the first 2 stanzas in the last stanza.  The elements of the Quaternion are:

  1. a poem in 12 lines made up of 3 quatrains.
  2. metered at the discretion of the poet.
  3. rhymed, aabb ccdd abcd.

    Third Dimension by Judi Van Gorder

    Forgotten in a tight airless attic,
    a thing that was to prove problematic,
    a Halloween reflective diorama
    in reenactment of a psychodrama.
    The shoebox, webbed and painted black,
    a tiny coffin's cedar lid drawn back,
    inside a body stiff in death, an ax
    embedded in the head, a final tax.
    A challenge to create this poematic
    with ghoulish display in frightful panorama.
    The sounds with screeching tone, elegiac
    and words don't always tell the lonely facts.

The Binary Tree is an invented verse form that borrows elements from both mathematics and computer science according to its creator Jason A Banico. In computer science the binary tree is like a family tree in which each "node" has 2 "children" or in this verse form a node is represented by a hemistich which is repeated. This 11 line poem is made up of 9 different phrases repeated at least once.  The elements of the Binary Tree are:

  1. a poem in 11 lines. The first 9 lines are written in hemistichs which includes at least one hemistich or phrase that is repeated elsewhere in the poem.
  2. metered at the discretion of the poet, obviously 2 versets, phrases or hemistichs must make up a line.
  3. unrhymed.
  4. composed with repetition, the first hemistich of L1 is repeated as the second hemistich in L2 and L5 and the first hemistich in L4, the 2nd hemistich of L2 is repeated as the first hemistich of L3 and L7 and the 2nd hemistich of L8. The first hemistich of L2 is repeated as the 2nd hemistich of L4 and the first hemistich of L6. The 2nd hemistich of L3 is repeated as the 2nd hemistich of L7 and the first hemistich of L9, the first hemistich of L5 is repeated as the first hemistich of L10, The 2nd hemistich of L6 is repeated as the 2nd hemistich of L10. The first hemistich of L8 is repeated as the first hemistich of L11 and the 2nd hemistich of L9 is repeated as the 2nd hemistich in L11.

    L1: a / b
    L2: c / a
    L3: b / d
    L4: a / c
    L5: e / a
    L6: c / f
    L7: b / d
    L8: g / b
    L9: d / h
    L10: e / f
    L11: g / h

    Starving by Judi Van Gorder

    The growl within, empty light,
    the clock strikes noon, the growl within,
    empty light, a need to feed
    the growl within, the clock strikes noon
    to plug the hole, the growl within
    the clock strikes noon, the lunch time boon,
    empty light, the need to feed
    sit down to eat, empty light
    a need to feed and fill up soon,
    to plug the hole, the lunch time boon
    sit down to eat and fill up soon.

The Tricube found at Writer's Digest is an invented form by Phillip Larrea is inspired by the mathematic "cube" to the third power.

The elements of the Tricube are:

  1.  a hexastich made up of 3 tercets.
  2.  a tercet is made up of 3 lines. (This obvious fact is spelled out in keeping with the third power concept.)
  3.  syllabic, each line is only 3 syllables long

    Conceived in Liberty by Judi Van Gorder

The Tritriplicata is an invented by Arjan Tupan, "Story Teller, Cross Pollinator, and Ideator" from Papenveer, Nederland, that focuses on 3 to the power of 3 or 3 times 9 = 27.   This form has a total of 27 syllables.  Tupan notes one reason for his focus on the number 3,  "The poet, the poem and the reader, a tripartite force that empowers meaning."  

The elements of the tritriplicata are:

  1.  a pentastich, a poem in 5 lines
  2.  syllabic, syllables per line, 3-6-9-6-3  = 27 syllables total
  3.  imagist in that the poem should be a snapshop image
  4.  composed with turn or volta

    elegy for humanity

    tears streak cheeks
    while sheets cover faces
    of fallen victims to a virus,
    filling lungs, stopping breath,
    killing us
              ~~ Judi Van Gorder

The Zeno is a recently invented form created by J. Patrick Lewis. "it was inspired by the mathematical “hailstone sequence,” simply explained here…. I call the form a “Zeno,” so named for Zeno, the philosopher of paradoxes, especially the dichotomy paradox, according to which getting anywhere involves first getting halfway there and then again halfway there, and so on ad infinitum."   

The elements of the Zeno are:

  1.  a decastich, a poem in 10 lines
  2.  syllabic,  syllables per line 8-4-2-1-4-2-1-4-2-1
  3.  rhymed,   x x x a x x a x x a,  x being unrhymed  or only L4, L7 and L10 (the one syllable lines) rhyme.

    Gutted  by  Judi Van Gorder

~~ © ~~ Poems by Judi Van Gorder ~~

For permission to use this work you can write to Tinker1111@icloud.com

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