Geometry of Rome, Florence, and Milan: An Artist’s Inquiry into Universal Building Blocks of Art and Architecture

Arriving in Italy and Diving Right in!

Last week I arrived in Rome with too much covid-19 travel paperwork, a very heavy backpack, a compass and straight-edge, and open mind. My residency will take place in Northern Italy, and focus on plants and animals specific to Val Taleggio in the Alps, and while there are specific and interesting architectural styles present in the Valley, which I will get into later, I wanted to pull into my research the broader Italian traditions within art and architecture to hopefully create more connections between the humans and animals who have been calling this place home for millenia. There have been many significant advances in architecture, engineering, and art made in Italy across history, so along with the pizzerias and gelato shops, I visited many of the most famous monuments and art museums here with a keen eye for the geometry and form.

Sacred Geometry: An Ancient Science

I was introduced to the science and history of sacred geometry only in the past couple years, yet it was no surprise how deeply significant geometry is to all things. Whether you’ve been studying sacred geometry for years, or it is a totally new concept to you, there is always indefinitely more to learn. Humans have been engaging with these concepts across cultures since symbols were first being drawn. Sacred geometry existed before us, exists within us, and will exist after us.

Considering that this sacred science has been studied and engaged with since time immemorial, there is a vast collection of media, literature, and knowledge surrounding the topic. I will be supplementing my observational research with a few books and spot researching online, but will be focusing more on what I am experiencing through my own eyes. I do not purport to be an expert nor does it make sense for me to attempt to consume thousands of years of research before I begin my own.

It is important to me, and is a value of NAHR that I go about my information gathering in ways that are easily accessible through embodied and field research and come naturally to a dropped in, engaged, and immersed mind. If you have further knowledge or connections to add to my observations, please, absolutely share your thoughts in a comment. Let’s have a conversation!

The Circle and the Seed

In my observations of Italy’s churches, institutions, and public gathering spaces, some as old as 500 BC, the dominant patterns that were visible to me related to the circle and the semicircle. The circle is the oldest shape. As the shadow of the sphere, it represents the seed, the egg, the earth, the sun, and the atom. The circle is the beginning. But how do we get from the circle to everything else?

The most common representation I’ve seen of how one becomes two is cell division. When a cell multiplies, there is a moment where two circles appear to cross, which creates a Venn-diagram-like shape called the vesica pisces.

This shape, significant on its own, also holds the potential for every other shape. The circle, which previously felt infinite and unbreakable has now been broken into sections, creating arcs and points with clear beginnings and endings.

In the vesica pisces, there are two points where the perimeters of the circles make contact. Using those two points as the origins of the next circles, a shape begins to take form, which when complete, becomes “the seed of life” resembling, most immediately, a six pointed star or a flower. This shape, among its many offerings, is an excellent representation of radial symmetry.

Radial symmetry can be found nearly everywhere it seems. Animals, flowers, and fruits carry this theme through in the natural landscape, and architecture mimics and builds upon these patterns as well. I was particularly struck by the Santa Maria del Fiore (below), one of the worlds largest cathedrals, in Florence. Not only is it surmounted by Brunelleschi’s dome, which utilizes radial symmetry, but it is also heavily adorned on the exterior with innumerable more examples.

Hoping for an up close view of the dome’s interior, I had staked out a spot in line, in front of the Biglietteria (ticket booth), and used the opportunity to scan the exterior with my binoculars. I was excited to find a fascinating band of circular designs tucked in the shadows under an upper balcony which wrapped around the side of the cathedral. Where most patterns repeated exactly the same one after the other, each circle in this particular row held a different design within it, nearly all using radial symmetry. There were 4 pointed crosses (tetramerous), flowers with 5 petals (pentamerous), 6 pointed stars (hexamerous), wheels with 8 sections (octamerous), and 7, 8, and 11 pointed pinwheels, but they were all linearly associated, circumscribed by congruent circles. To me this represents that unity and diversity can and often coexist, a theme with I am sure will continue to come up throughout my project.

Look closely for this row below the balcony in the following video. What do these forms remind you of? How many additional instances of radial symmetry can you see? My favorite instance of radial symmetry is just above the last set of windows. I have attempted to draw it as well using classical geometry: Using only a compass and a straightedge.

While all different varieties of radial symmetry were cropping up within the architecture of Rome and Florence, the most common variety was octamerous, followed closely by hexamerous radial symmetry. In Rome, I visited the Capuchin Crypt, an overwhelming and intricate 6 room installation constructed from at least 3,000 de- and re-constructed skeletons of deceased Capuchin friars. The organization of the bones was highly geometric. One placard stated that the skeletal 8 pointed stars represented “the morning star” or Mary, Mother of Jesus.

Though not exclusively, most domes in both Rome and Florence were octamerous- each point of an octagon drawn together to an apex. This form was clearly an architectural staple in Italy, as it is in many places around the world. Italian engineers, like Leonardo da Vinci, made advances specifically in the scale of domes that could be constructed while remaining structurally sound.

Halving the Circle: Domes, Arches, and More

By looking at a dome from above or below, we see its radial symmetry, but by imagining the cross section of the dome, we get the shape of an arch- which was even more common throughout architecture new and old, and a predecessor to the dome. I saw rounded arches, pointed arches, and arches containing a trimerously symmetric shape representing the holy trinity, visible in the arches in the above video of the Santa Maria del Fiore. This holy trinity shape is created by joining three vesias, the central shape of the vesica pisces.

Another place where I thought I might find the vesica pisces hidden was not in an arch, but in a pattern of arcs, created in the cobblestones in both Rome and Milan. This design wasn’t present on every cobblestone street where most used very linear patterns, but each use of this fan-like pattern stood out to me as I zipped through the city on a rented electric scooter, my teeth chattering together with each stone I rode over.

Cobblestones near the Pantheon in Rome
Cobblestones in the courtyard of my Air Bnb in Milan

Because I recognized each arc as a section of a circle, I was looking for a way to follow the arcs past their intersection points into a more complete shape. I spent a long time following each arc to where it met the next, and realized that the intersection points were organized a bit haphazardly, yet on a macro scale this aspect wasn’t so apparent. Unable to draw many clear conclusions through observation, I imported the photos to a digital drawing program, completing the circles, then trying to understand if a more complete pattern could be created with more precise calculations. I thought the square stones may have been limiting in their orientation so I used circles to represent stones instead. These digital drawings only further confirmed that the points of intersection created difficulties when it came to the spacing of stones.

Arches and arcs were clearly not hard to come by in ancient Rome. Arches were used as support systems for aqueducts, and in altars and fountains, but the most common way I saw them used were to surround windows and doorways. One basic architectural pattern I saw repeated over was similar to the following drawing:

In addition to the common arched window pattern, I also noticed that most buildings had 3 stories of equal height. It’s likely that 3 stories is what the technology allowed for in a standard dwelling, and that there was no need for more, but it was a reminder to me of the rule of thirds. The rule of thirds is an approximated and simplified version of the golden ratio, yet both indicate aesthetically harmonious composition.

The Golden Ratio: The Mathematics of Art and Humans

The golden ratio, also known as phi, has been significant in the creation of many things because it creates a perfect sense of balance. It can be found when the ratio of two unequal parts (a and b) is equal to the ratio of the larger part to the whole (b and c). This ratio always comes out to an irrational number of approximately 1.618 (b/a=1.618… and c/b=1.618…). The rule of thirds approximates it with the ratio of the larger part to the whole equaling 1.5 (c/b=1.5).

a is to b as b is to c

Another way the this ratio is commonly represented is by the Fibonacci spiral. In my preparations for my trip I found two compositional viewfinders for finding golden ratios and thirds in your field of view. The Fibonacci spiral (seen in the blue looking glass) is a well-known representation of the golden ratio because it visualizes numbers increasing by the golden ratio as adjacent squares. This sequence of numbers, called the Fibonacci sequence, as well as the spiral representation was brought from the Middle East to Europe by Leonardo Bonnaci, who is also credited for contributing to the popularization of the Arabic numerals we use today over the more cumbersome roman numerals.

Fibonacci spiral
Compositional viewfinders

Leonardo da Vinci, who knew about, used, and contributed to study on the golden ratio, was very interested in spirals, studying them intensely in his drawing and painting (source), as well as in engineering. In my visit to the Leonard da Vinci museum in Florence (fun fact, there are two unassociated Da Vinci Museums on the same block), I saw examples of his early air screw (an early helicopter design), as well as the Archimedes Screw, a machine engineered for moving water uphill, which fascinated him. Da Vinci was also using the golden ratio and geometry in his paintings and drawings, famously including The Last Supper and the Vitruvian man.

Vitruvian Man by da Vinci

Other artists of the Renaissance were also using the golden ratio in painting. I tested out my viewfinder in the Uffizi Gallery on Botticelli’s The Birth of Venus as well as some Michelangelo paintings and easily found the ratio hidden within the bodies and faces of their subjects. Michelangelo’s famous statue of David, which I was able to visit at the Galleria dell’Accademica, was created with the golden ratio in mind in order to create the epitome of human beauty. I found David, to be astounding in person. The curvatures, shadows, and human likeness of the statue was surreal. It felt balanced, alive, and aesthetically satisfying. The work of Michelangelo, like Da Vinci’s, was very tied to geometry and mathematics. I was also very intrigued by the courtyard he designed on Capitoline Hill (below), which I visited in Rome.

But you don’t have to go all the way to Florence for the statue of David to find the golden ratio (and the vesica pisces) in the human body. Just look at your eye shape in a mirror, or check out the ratio from your forearm to your hand or between your knuckles with a ruler, then use the formulas above to see if you get something close! The golden ratio is hidden everywhere in our bodies. I’m looking forward to seeing where else I can find these shapes when I explore the nature of the Alps in the coming weeks.

After visiting these masterpieces, some of which were carefully preserved while others were weather worn and in ruin, I am left with questions about the importance of preserving culture and artifacts and the accumulation of man-made objects. Perhaps I would be feeling differently had I visited the Mall of America instead, but the topic of preservation is one I will surely ruminate on as I begin my own creative process of making work that will decidedly not be preserved.

Lilia Deering (She/Her) is an LA based artist with a focus in environment design within a variety of contexts including the stage, the gallery, film, and experiences. Coming from a background in dance and performing arts, Deering’s overall goal is to push boundaries in world-building and visual storytelling. She is interested in collaborating with diverse creative minds, and is not limited by any single medium, experimenting with various materials and technologies to spark curiosity and ignite the imagination.


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