# Poetic Forms Based on Mathematical Concepts: Line, Triangle, Square, Cube, Spiral, Möbius strip, and circle

Many poetic forms are syllabic or lexical, ie their designs call for specific formats. The inventors of the following poetic forms, however, drew heavily on the field of mathematics for the design and often even the naming of the forms. The following is only a short list of poems that found their basis in mathematics.

SUZETTE PRIME: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. As with the Fibonacci sequence (see below), prime numbers are also found in nature: It was found that cicadas only leave their burrows at intervals of 7, 13, or 17 years, depending on the species.

© Suzette Prime 2012, an invented form by Suzette Richards, was introduced at PoetrySoup.com as a new poetic form in December 2012. The design: Prime number syllable format: 2-3-5-7-11, etc; PLUS a philosophical statement. Any combination of a prime number syllable count may be used per line; in open form/free verse and no formal stanzas; in lower case, unless it is a proper noun; no punctuation used, and presented flush left on the page.

TETRACTYS: Euclid of Alexandria (Mid-4th century BC—Mid-3rd century BC), the great Classical mathematician, believed that the numbers 1, 2, 3 & 4 must have some mystical significance because their sum total is 10—ten was thought to be a number of power. He called this relationship a tetractys.

The Tetractys, named after this, is a syllabic poem designed by the English poet Ray Stebbing; written with 20 syllables in total. In any formatting (centred on the page or flush left/right), it will give a triangle shape. The design:

1. The syllable format: 1 (NB: Don’t use an article) -2-3-4-10 per the lines;

2. the rhythm of the first four phrases is isochronic (coming at regular, brief intervals) with a single stress arc each, ie it must be meaningful phrases;

3. use of poetic devices, eg rhyme at L5/L6 when longer poems are designed;

4. lastly, and most importantly, appeal to the intellect and the emotions; moving the reader to laughter, tears, deep thought, or anger, all in one statement.

There is no limit to the number of stanzas: It can be reversed, starting with the ten-syllable line, for a ‘reversed Tetractys’; or the ‘double Tetractys’ in which two stanzas follow immediately upon one another; and a normal Tetractys followed by a reversed Tetractys which would give you a diamond shape if centred. There is no white space between the stanzas. The title (1 syllable) is derived from the first line of the poem.

TRICUBE: TriCube is an invented form by the USA journalist Phillip Larrea, which was introduced at Writer’s Digest in January 2016. Each line contains 3 syllables; each stanza contains 3 lines; and each poem contains 3 stanzas. There are no set rules regarding rhymes, metre, etc. Each stanza reads like a phrase (not disjointed clauses), and it is written on the same topic.

SATOR SQUARE: The Sator Square, consists of a sentence written in Latin: Sator Arepo Tenet Opera Rotas. Sator is the first word of a well-known Latin palindrome (invented by Sotades in 3rd-century BC Egypt). One of the translations is: ‘The sower Arepo leads the plough with his hand’. It is remarkable for the fact that the first letters of each word form the first word, the second letters form the second word, and so forth. Hence, it can be arranged into a word square that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left.

LOK SQUARE: One of the earliest examples of visual poetry is the classic Lok Square created in 1597.  A square in verse of a hundred monasillbles [sic] only: Describing the sense of England's happiness, written in Honour of Elizabeth I by poet Henry Lok.

(You may Google the image of the Lok square.)

FIBONACCI POEM: In mathematics, the Fibonacci Numbers/Fibonacci Series/Fibonacci sequence is the numbers in the following integer sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21 … The Fibonacci sequence appears often in nature, for example, in sunflowers. It is named after its Italian founder, Leonardo Fibonacci.

Fibonacci poems (syllabic OR lexical poems) can embrace the number sequence in two ways, either in numbers of syllables or in numbers of words. Ie, write the poems so that each line contains the number of words of its place in the sequence, OR use the sequence to determine the number of syllables in each line.

FIB: The shorter fib poem, created by Gregory K Pincus in 2006, is written in as few as 6 lines, with 20 syllables in total, in keeping with the Fibonacci sequence.

PHI POEM: Phi (φ 1.618033988749895…) is most often pronounced fi like ‘fly’.

The golden ratio is about 1.618, and is represented by the Greek letter phi, φ. That is, (a + b)/a = a/b. These elements inspired the design of the Phi poem.

The spiral pattern created from the golden ratio is also called the golden spiral and its symbol has been associated throughout history with the fundamentals of life, spirituality, and creation. The Fibonacci spiral is related to but not identical to the golden spiral. 'The golden spiral has constant arm-radius angle and continuous curvature, while the Fibonacci spiral has cyclic varying arm-radius angle and discontinuous curvature.'* The Fibonacci sequence was the inspiration for a poetic form in its own right (see above).

The © Phi poem is a 5-line syllabic poem with a rhyme scheme, invented by Suzette Richards, 2021. The 4th line should enhance the concluding word (in caps) by using any number of poetic devices at your disposal. Presented centred on the page.

• Rhyme scheme: a1 + b; a2; a3; b; x. (L1:  = an internal rhyme that cross rhymes with L2 & L3.) "x" = no rhyme.
• Syllabic format of first 3 lines: 1 + 6; 1; 8; L4 & L5 are any number of syllables.

MOBIUS POEM: The Mobius [sic] poem, lexical poetic form, was created by Celtic~Soul (A penname). The name Mobius* was derived from the ability to read the verse, i.e. when one reaches the last word and returns to the first line, the verse flows to begin again in a poetic, logical sense. Words in the list lines should relate to the previous and following statement lines so that the poem reads smoothly. Mobius poems have six or more lines that alternate as follows:
• Statement line (for example ‘a childlike belief’)
• List line (for example ‘artless, trusting, pure, timeless’)
Each list line must end in a ‘time word’ (day, night, eternity, hour, etc). This ‘time word’ should be italicised. The last word of the final line, whether list or statement line, should be a noun that refers to the poem’s title and flows back into the poem’s first line, for example ‘embracing innocence’. Mobius poems are the best presented in a centred format AND in lowercase.

*The Möbius strip or Möbius band has the mathematical property of being non-orientable. It can be realised as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858. The Euler characteristic of the Möbius strip is zero.

EINTOU: It represents the circle. The term Eintou is West African for ‘pearl’ as in ‘pearls of wisdom’. The Eintou is a seven-line African-American poetry form. The design: The syllable format: 2-4-6-8-6-4-2 per line. It is centred on the page for the best effect. The Eintou can be considered a form of protest; creating a poetic form for African American poets to use, without forcing them into the Eurocentric tradition of poetry. The Eintou is concerned with sharing knowledge. It should be used to offer insight and challenge the way we see the world but is always respectful in the treatment of the subject.

INTERSECTION/VENN DIAGRAM POEM: Depicted above. Venn diagrams consist of two or more shapes (usually circles) to illustrate the relationship between two or more sets of data, where the intersection highlights the commonality of the different sets, popularised by John Venn in the 1880s.

The Venn diagram poem is an interesting intersecting visual poem written inside a two-circle Venn diagram. In the absence of a Venn diagram template, the three sections could be formatted side by side on the page, with the intersection in italics. It could be written on any subject where a contrasting viewpoint is key to a successful intersection poem. The idea is for the two outer sections to be read independently, taking the intersection into account: Eg xxxxxxx X / X xxxxxxxx. This intersected piece ‘X’ should flow in a logical statement from top to bottom. My poem was inspired by the Bilston intersection poem,* and it may be viewed at my website Suzette: Poet:

CIRCUMLOCUTION

*In the 2015 Great British Write Off, Brian Bilston won the poetry prize for a poem disguised in a Venn diagram: Him & Her Intersection.

PILISH: Pilish is a form of constrained writing that straddles the boundary between language and mathematics. Pilish literature is written in such a way that the number of letters in each successive word corresponds to the digits of pi, beginning with the number ‘3’, and then followed by the successive decimal places of pi. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. 14 March is celebrated in the USA as National Pi Day, because of the particular way dates are written: 3/14…

MY EXAMPLE: 3.14159265358979323846264338327950

For a love I would sacrifice my sanity, sleep and whole lifetime dedicated efforts; heartache won in the meantime from cradle to rubout life; you are innocent not to requite ingenious angel.

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*Research Article | Open Access

Volume 2019 |Article ID 3149602

Jun-Sheng Duan

School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China