Thoughts So, let's dissect this. There's a lot of science going on in this poem. First, the title. 1.6180339... is the Golden Ratio, an irrational number. (It has many other names: Golden Mean; Golden Spiral; Divine Proportion... and is represented by the Greek letter phi, φ). Two numbers describing a rectangle will reflect the Golden Ratio if the ratio of the long side divided by the short side is the same as the ratio of the sum of the sides divided by the long side. The example in the poem is 5 and 8, two numbers in the Fibonacci Sequence also referred to here. So, 8/5 will approximate 13/8. The Fibonacci Sequence is a series of numbers where each number is the sum of the preceding two, beginning with 0 and 1 e.g., 0, 1, 1, 2, 3, 5, 8, 13.... Dividing any Fibonacci number by its predecessor will approximate the Golden Ratio, becoming closer to 1.618... with increasingly larger Fibonacci numbers, e.g., 55/34 ≈ 1.61764... and next in line 89/55 ≈ 1.61818... (Fibonacci was an Italian mathematician also known as Leonardo Pisano... hence the intro to the poem). Let's move on. The Elements refers to the mathematical treatise of Euclid, written around 300 BCE, a collection of 13 books bringing together postulates, algorithms etc. produced by many early mathematicians (such as Pythagoras and many others). The Elements represent the foundation to this day of what we call, appropriately, Euclidian geometry (the geometry most of us learn in school). Euclid described the Golden Ratio within the Elements, though he used the term 'extreme and mean ratio'. And then we have 'Penrose's tiles, and five-fold symmetry', a reference to a geometric form discovered in 1974 by Sir Roger Penrose, a 20th c. British mathematician and Nobel laureate in physics. Penrose tiles are geometric forms ("tiles") created by two adjoining shapes (called kites and darts, which is what they look like!). As the Penrose tile expands, adding more kites and darts, the ratio of the number of kites and darts approximates 1.618... in other words, the Golden Ratio! And five-fold symmetry is a property of a Penrose tile, in that one can rotate a tile by 72 degrees (360 degrees/5!) and the tile will always appear the same. So, what has all of this to do with cresting waves at Punakaiki, found on the South Island of New Zealand, or Andromeda's sweeping arms? Simply that the curve of breaking waves and the curved arms of spiral galaxies reflect what is known as the Golden Spiral - and as the spiral grows in size, it grows as per the Golden Ratio. Indeed, the Golden Ratio is ubiquitous in nature, from the arrangement of sunflower seeds in their pod, to flower petals themselves, to the chambers of a Nautilus shell, to the universe itself – and even in your own body, as the ratio of the distance from your navel to your feet relative to your total height! And there you have it! Annerose Georgeson is a visual artist living in northern British Columbia, Canada. She can be found online at https://annerosegeorgeson.com/. This piece is from my own collection and is used with permission of the artist.