Among the many striking artifacts discovered at Pompeii is the famous SATOR square, a five word palindrome that can be read from top to bottom, bottom to top, left to right and right to left:

There has been much scholarly speculation about the origins, meaning and significance of the SATOR square, but viewed as a form of mathematical poetry its elegant ingenuity cannot be disputed. One possible translation of the inscription is: The farmer Arepo holds wheels as his work, presumably for the purpose of ploughing the land.

The possibilities inherent in the square poem structure have attracted poets through the centuries, including Elizabethan poet Henry Lok, Charles Lutwidge Dodgson (Lewis Carroll) and H. L. Hix.

A search for ‘square poems’ on JoAnne Growney’s brilliant blog Intersections – Poetry with Mathematics will provide links to a number of examples of the form, including several delightful poems by Growney herself. Her 5 x 5 syllable square poem ‘Counting the women’ (reproduced here with her permission) is a wry comment on the paucity of women in mathematics and other STEM subjects:

     When I look around
     the room – if I don't
     know in one glance how
     many women are
     there with me, I smile.

Recent years have seen the emergence of innovative forms of square poetry, including the grid poem, conceived by Brian Isett, and the Latin square puzzle poem and its more challenging variation, the Graeco-Latin square puzzle poem, both of which were devised by the Canadian mathematician and poet Lisa Lajeunesse.

Bob Cobbing’s witty concrete take on the square poem consists of 12 lines, each of which is a permutation of the five words ‘This is a square poem’. Through Cobbing’s artful choice of font, spacing and punctuation, the poem forms a geometric square. 

By its nature, visual poetry lends itself to geometric associations. Artist and visual poet Laura Kerr drew inspiration from Pythagoras – ‘There is geometry in the humming of the strings, there is music in the spacing of the spheres’ – to create the stunning square poem below (reproduced here with her permission):

References and further reading:

Birken, Marcia and Coon, Anne C. (2008) Discovering Patterns in Mathematics and Poetry, Amsterdam, Rodopi.

Fishwick, Duncan (1964) ‘On the Origin of the Rotas-Sator Square.’ The Harvard Theological Review, vol. 57, no. 1, 1964, pp. 39–53.  http://docshare02.docshare.tips/files/16340/163404657.pdf

Glaz, Sarah (2012) ‘Mathematical Pattern Poetry.’ Bridges 2012 Conference Proceedings http://m.archive.bridgesmathart.org/2012/bridges2012-65.pdf

Coxson, G. E. ‘JoAnne Growney’s Poetry-With-Mathematics Blog — An Appreciation,’ Journal of Humanistic Mathematics, Volume 2 Issue 2 (July 2012), pages 140-150. DOI: 10.5642/ jhummath.201202.12. Available at: https://scholarship.claremont.edu/jhm/vol2/iss2/12

Hix, H. L. (2000) Rational Numbers, Truman State University Press

Lajeunesse, Lisa (2019) ‘Graeco-Latin Square Poems.’ Bridges 2019 Conference Proceedingshttp://archive.bridgesmathart.org/2019/bridges2019-35.pdf

Lajeunesse, Lisa (2018) ‘Poetry Puzzles’. Bridges 2018 Conference Proceedings http://archive.bridgesmathart.org/2018/bridges2018-645.pdf

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

Motoyama, Hiroshi (2001) Theories of the Chakras. New Age Books, Delhi

Plato, Timaeus and Critias, tr. Desmond Lee (1965). Penguin Classics, Middlesex

Updated on 20th August 2021. This is a summary of my former blog post on Square Poems.