For me, the archetypical example of the intersection of art and science (and math) is the sequence of numbers commonly called the “Fibonacci numbers.” By definition it is the sum of the previous two numbers in a series. So, it gets started with 0 and 1, and then picks up speed. Next is 1, then 2, then, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The sequence plays out visually in things we may encounter every day, like in the spin of the Milky Way or the magnitude of the increasing size in a chambered nautilus shell.
The following link is a gorgeous visual of the occurrence, beauty and magnificence of the diversity in nature that illustrates and validates the Fibonacci series. Click the link and then click on “Nature by the Numbers.” Mathematics in Sunflowers Shubha Bala, associate….
“Ideal proportion” and the geometry of visually pleasing balance is also suggested by the Fibonacci series. It correlates to how we perceive things that are beautiful and balanced. For example, Leonardo da Vinci’s Vitruvian Man, demonstrates the proportions of the human body that (at least at that time in the 15th Century) were considered ideal.
The illustration of a fellow from Tuscany (who knows he may have been from Florence, or da Vinci’s town, Vinci) presents a drawing of someone who was well proportioned and elegantly composed within a circle. Here da Vinci, who was an inventor and engineer as well as an artist, created an illustration that was not only a masterful expression of the human body, but also suggests a parallel and masterful design of a balanced and harmonious universe.
Traditionally-trained artists–even today–spend plenty of time in drawing classes learning about proportion and balance, and in working within the divisions, ratios and “chambers” of a visual composition. They may not know that a primary source for what seems pleasing to a Western sensibility is carried forward by the repetition of the concepts portrayed by da Vinci in the geometry and balance of Vitruvian Man.
And now, perhaps the underlying sense of what is balanced and pleasing to the eye has been permanently ingrained in us, as quantified by us via the Fibonacci series, and illustrated by da Vinci. Yet, it still makes us consider the hidden mathematical sequences in nature and therefore the predictability in the patterns of the seeds growing in sunflowers… it is so awe-inspiring that it’s calming and invigorating at the same time.
Image of Vitruvian Man from Wikimedia Commons, a freely licensed media file depository, licensed through Creative Commons. Accessed June 14, 2010. <http://en.wikipedia.org/wiki/File:Da_Vinci_Vitruve_Luc_Viatour.jpg>