Sometime around 1550 BC an Egyptian scribe named Ahmes noted down a method for obtaining the area of a circle, in what is the earliest recorded attempt to evaluate the number we know as 𝜋.

The history of 𝜋 (its symbol is the Greek letter pi) is fascinating, as are its many applications in poetry. To 16 digits, the expansion of 𝜋 is

𝜋 = 3.141592653589793.

Pre-calculator days, mnemonics known as ‘piems’ (pi-poems) were sometimes used to commit to memory the value of 𝜋 to a given number of digits. The Wikipedia article on Piphilology provides many delightful examples, including several in languages other than English. A recent variation of the piem is the piku, which has several versions, all constrained in varying ways according to the expansion of 𝜋.

Jacques Bens, a founding member of the Oulipo movement, invented the sonnet irrationnel – irrational sonnet – which has five stanzas of 3, 1, 4, 1 and 5 lines respectively (the first five digits of 𝜋, adding up to a total of 14 lines) and also conforms to specific rhyme and metrical patterns. Rachel Galvin has translated seven of his irrational sonnets into English, the first of which can also be read here in the original French.

A set of rules, known as Pilish and explained here by the American mathematician Mike Keith, has been developed for writing constrained by successive digits of 𝜋. Keith has produced several remarkable works of constrained writing in Pilish, including a novel, a retelling of Edgar Allan Poe’s ‘The Raven’ and a circle poem using the first 402 digits of 𝜋. He has also created his own elegant version of the piku.

A fascinating paper by Dr Tatiana Bonch-Osmolovskaya explores several other applications of 𝜋 in literature, including examples of Russian poetry by herself and others.

Experimental poet and publisher Anthony Etherin frequently makes use of mathematical constraints in his writing. He is the inventor of the aelindrome, an extension of the palindrome in which words are divided according to a specific numerical sequence into letter units, that are then reversed around a pivot. His aelindrome ‘Asymptote’ is structured around the expansion of the exponential constant *e *= 2.7182818284590452353…:

There are many other mathematical sequences that have informed poetic structure (including the Fibonacci sequence, subject of an earlier blog post). . The simple additive sequence 1, 2, 3, … is used to construct ‘snowball poems’, applying an Oulipian constraint in which each line consists of a single word, with each successive word one letter longer. There is a discussion of this form with several interesting examples on JoAnne Growney’s website Intersections – Poetry with Mathematics.

Daniel Tammet has observed that the traditional Japanese poetic forms the haiku and the tanka both use prime number sequences in their structure. In her excellent overview paper ‘Poems structured by integer sequences’, Sarah Glaz discusses this and other applications of prime number sequences in poetry.

Another mathematical sequence, formed from the coefficients of binomial expansions, is commonly presented as an array known as Pascal’s Triangle. Emily Galvin’s poem ‘Pascal’s Triangle’ uses this structure in the arrangement of the stanzas. Pascal’s Triangle also provides the architecture for my two poems ‘Midwinter’ and ‘Autumn Sunrise’.

A striking illustration of the creative synergy that can exist between art, poetry and mathematics is artist Carl Andre’s poem ‘On the Sadness’, which is structured according to the Fundamental Theorem of Arithmetic. Both Sarah Glaz and JoAnne Growney have also written poems using this structure. In a fascinating interdisciplinary collaboration, three of Growney’s poems, including this one, have been paired with artwork by Allen Hirsh.

The earliest proof of the Fundamental Theorem of Arithmetic dates back to Euclid, who was born in the 4^{th} Century BC and died in Alexandria. As in the case of the scribe Ahmes estimating a value for 𝜋 over a millennium earlier, this illustrates how poetry and mathematics can intertwine across centuries, continents and cultures.

**References and further reading**

Blatner, David (1997) *The Joy of **π.* Penguin Books

Bonch-Olovskaya, Dr Tatiana (2012) ‘Art of π: Mathematical History and Literary Inspiration’,* Proceedings of Bridges 2012.* Available online at http://archive.bridgesmathart.org/2012/bridges2012-79.pdf

Etherin, Anthony (2017) *Aelindromes*. Available online at https://anthonyetherin.files.wordpress.com/2017/07/aelindromes.pdf

Etherin, Anthony (2019) *Stray Arts (and Other Inventions).* Penteract Press

Galvin, Emily (2008) *Do the Math*. Tupelo Press, Vermont

Glaz, Sarah, and Growney, JoAnne (eds.) (2008) *Strange Attractors: Poems of Love and Mathematics*. A.K. Peters, Massachusetts

Glaz, Sarah (2011) ‘The Poetry of Prime Numbers’, *Proceedings of Bridges 2011*. Available online at https://archive.bridgesmathart.org/2011/bridges2011-17.pdf

Glaz, Sarah (2016) ‘Poems structured by integer sequences’, *Journal of Mathematics and the Arts*, 10:1-4, 44-5.

Glaz, Sarah (2017) *Ode to Numbers.* Antrim House, Connecticut

Gourévitch, Boris, *The world of π.* Available online at http://www.pi314.net/eng/index.php

Growney, JoAnne, *Intersections – Poetry with Mathematics.* Available online at https://poetrywithmathematics.blogspot.com

Keith, Mike, *Web Home of Mike Keith*. Available online at http://www.cadaeic.net

May D. (2020) ‘Poems Structured by Mathematics’ in: Sriraman B. (eds) *Handbook of the Mathematics of the Arts and Sciences. *Springer, Cham.

Tammet, Daniel (2012) *Thinking in Numbers*. Hodder & Stoughton

*Updated on 20th August 2021. This is a summary of my former blog post on Number Sequences in poetry.*