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 swirling cream in a cup of coffee and even the ordinary sunflower so abundant on the Midwestern plains in the summer.
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 here to see an astonishing animation about math in the formation of nature.” “Nature by the Numbers” by Christobal Vila..
“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, Milan, or da Vinci’s town, Vinci) presents a drawing of someone who was well proportioned and elegantly composed within a circle within a square.
In a 2017 book by Walter Isaacson, he suggests that the model for Vitruvian Man may have been da Vinci himself. 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 mathematical 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. History shows us that it has been carried forward by the repetition of the concepts portrayed by da Vinci in the geometry and balance of Vitruvian Man, which itself was founded on early works from the Romans.
And now, perhaps the underlying sense of what is balanced and pleasing to the eye has been permanently ingrained in us, as illustrated and quantified by 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 awe-inspiring and a bit of a dichotomy since it’s calming and invigorating at the same time.
As an update to this post about the Fibonacci number series, illustrating how math, and geometry have an elegant relationship to art. The Science Museum of Minnesota launchedg a Special Exhibition, “Geometry Playground,” 10/15/2010.
Here’s the overview from the website: “The Geometry Playground exhibition will change the way you think about geometry, letting you use your hands, brain, and body to play with physical demonstrations of this often ‘textbook subject.'” So the Science Museum is adding another sensory experience to synthesize the concept of geometry; a playful way to invite participation in experiencing geometry. Sounds like fun!
Regarding geometry and its relation to art, in the summer semester of 2010, I presented a program on art and geometry at a third-grade summer-school class in St. Paul, MN. We talked about handmade quilts and the geometry involved in the design, artistry and construction of the quilts. The third-graders delighted in the surprise of seeing the squares, triangles, hexagons, and rectangles in the quilts. And since there were 16 students in the group, it was an ideal teaching opportunity to bring the concept of square numbers (i.e. 4 x 4) into the discussion. A beautiful way to bring geometry, math, art and an American craft to a group of students.