The scent of lilies at night made me feel like a voyeur as I walked along someone’s garden on the way back to the car after the  fireworks ended. I spied the thick petals rising over the ferns to bathe in the night air, the greenness of the ferns a perfect foil. This being July, the unfurling was mostly done, but the knowledge that the unfurling patterns followed the Fibonacci sequence made the world of numbers come alive in spite of a lack of moonlight. As you know. each number in Fibonacci sequences equals to the sum of the two preceding numbers.  Mathematically,  Fn = Fn-1 + Fn-2. The Fibonacci sequence of order 2 (n =2) includes 0, 1, 3,5,8,13,21 … This series abounds in nature: the calla lily has one petal, euphorbia two,  buttercup five, delphinium eight, black-eye susan thirteen, aster twenty one. Is it the number of petals in the flowers that make them pleasing to the eye, or is there something else?  Perhaps, because the sun flowers actually have their seeds packed that way to maximize the number of seeds in that space with the angle between the appearance of each seed exactly the one that is least approximated by a fraction, the golden angle calculated from the golden means which is the ratio of two successive numbers in a Fibonacci sequence ^[1] .  It is the golden ratio Phi that creates the enduring beauty of the Parthenon, and underpins the face of the beloved.  How does a specific mathematical proportion cause a universal perception of beauty in the mind?  Will this poem shed some light on the bridge that links mathematics and beauty in the mind?

The tension in alternating the mind as both subject and object, enchanting and enchanted leaves me optimistic, especially the last line because by changing, the mind can create changes. By applying the golden ratio observed in nature to man made structures, we create beauty. That there are mathematical sequences behind beauty is encouraging because they add to the understanding of how we come to be and how we endure without depending on the existence of God, even though the comfort of believing in a greater being beckons as I mourn my mother. This series of posts has never been intended to be a journal, but I must mark her passing this past April. It took me several months to write again. This post is for you, mama, you who taught me how to solve for x by working out simple ratios, you who bought me many books of poems, explained to me the two-seven-six-eight meter in ca-dao, made potpourri for me from the roses in your garden, and most of all you who loved me unconditionally. I do not know if there is an afterlife, but I am grateful that your love of languages and things of beauty live on in me.

Thank you for the inspiration, dear muse.

Acknowledgments

1. http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html
2. The composite graphics of the sun flower is from http://www.mi.sanu.ac.rs/vismath/lends/ch2.htm and http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html
3. The fern photo is from http://www.flickr.com/photos/22887580@N06/2198052702/?reg=
4. The Fibonacci diagram is from http://www.learncpp.com/cpp-tutorial/710-recursion/
5. The Parthenon photo is from http://alexorbit.com/fibonacci/golden-ratio.htm