The Golden Ratio, denoted by the Greek letter *phi, *is an irrational number that has intrigued mathematicians and artists through the centuries, featuring in geometry, number theory, physics, biology, painting, architecture, music and other disciplines. Its value to 20 digits is

# Turning in circles – the Tritina

Repetitions are a feature of many established poetic forms – the triolet, pantoum, and villanelle all contain patterns of repeated lines, while the ghazal consists of couplets with a repeated refrain. The sestina is determined by six end-words, following a fixed rotational pattern through six six-line stanzas, with a three-line envoi that includes all the end-words.

Continue reading# Playing to our own rules: Poetic constraint

*Arma virumque cano* – ‘I sing of arms and the man’. With these resonant words Virgil opens his great epic the *Aeneid*, composed over two thousand years ago. The poem, which is nearly ten thousand lines long, is written almost entirely in dactylic hexameter – an astonishing feat of constrained writing, especially when we consider that Virgil lacked the convenience of our modern-day word processing and editing tools.

# Routes through a poem

Sometime during the fourth century, in northwest China, a woman named Su Hui picked up her silk thread and embarked on an embroidery project. The result was an extraordinary work of visual poetry – a grid of 29 x 29 characters, shuttle-woven on brocade to form a palindrome poem that would become known as *Xuanji Tu*, or the ‘Star Gauge’.

# Farewell to 2021

As we approach the end of a year dominated by chaos, bleakness, and the ravages of the pandemic, it is difficult not to succumb to despair. We seem to be caught up in the ‘widening gyre’ of Yeats:

Things fall apart; the centre cannot hold; Mere anarchy is loosed upon the world

Yeats wrote ‘The Second Coming’ in January 1919, at a time when the First World War had only recently ended, the political situation in his native Ireland was dangerously unstable and the Spanish ‘flu pandemic was raging (his pregnant wife Georgie Hyde-Lees became very ill and almost died from the ‘flu). It’s hardly surprising that a sense of impending doom reverberates through the poem.

Continue reading# Conics and Kisses: Poetry shaped by Apollonius of Perga

I used to loathe coordinate geometry at school, mainly because we had to calculate, plot and draw the graphs by hand. My geometry notebooks were full of wobbly parabolas and ellipses that staggered uncertainly from point to point rather than flowing in one smooth, continuous curve.

Continue reading# Poetry and Fractals

In his 1982 book ‘*The Fractal Geometry of Nature’* the mathematician Benoit Mandelbrot explored ‘irregular and fragmented patterns around us’ that ‘tend to be *scaling*, implying that the degree of their irregularity and/or fragmentation is identical at all scales.’

He called this family of shapes fractals, from the Latin adjective *fractus*, meaning fragmented or irregular. Such objects, Mandelbrot noted, are present in nature as well as in a wide range of fields.

# Intersections – Poetry, Mathematics and JoAnne Growney

Emmy Noether was one of the great mathematicians of the early 20^{th} century. Born in Bavaria in 1882, she loved dancing and initially trained to be a language teacher before opting, despite numerous obstacles, to study mathematics at university. She went on to make significant contributions in many areas of mathematics and mathematical physics, most notably in the field of abstract algebra.

# Mathematical forms in poetry 5 – number sequences

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.

Continue reading# Mathematical forms in poetry 4 – Permutations

Permutations are a feature of many poetic forms: rhyme and metrical patterns, the arrangement of lines in a villanelle or pantoum, the rotation of end-words through the stanzas of a sestina. Ruth Holzer’s ‘*For Dylan Thomas on His Hundredth Birthday’* is an example of a sestina by a contemporary poet, with end-words* wild, sky*, *end*, *hills*, *wave*, *love*.