Art in the Spirit of Geometry
- calypsolg9
- Apr 29
- 14 min read
Updated: May 8
Geometry is nature’s native tongue – a code woven through culture, spirituality, science and art. This review traces six artists who reimagine ancient forms for the present, inviting us to see the world afresh.
Index of Artists: click on an artist to jump to their section.
Introduction
In his polemic Il Saggiatore (1623), Galileo wrote:
"Philosophy is written in this grand book – I mean the universe – which stands continually open to our gaze. It is written in the language of mathematics, and its symbols are triangles, circles and other geometries. Without comprehending this language and interpreting it, one wanders in vain through a dark labyrinth".
Galileo – a man whose work cut across art, philosophy, astronomy, physics, biology, and engineering – couldn’t be a more fitting guide to begin with. He understood that to learn the language of the universe is to bring light to the foggy maze of life. In Galileo’s view, Geometry is not just a tool but a key: a way to navigate our outer and inner worlds.
This essay follows six contemporary artists who, in their own distinct ways, have picked up that key. Each works with a particular geometric form to sense, shape, and reimagine the world around them. Their practices dissolve the neat border between art and science, logic and intuition.
If science is a system for understanding how the world works, these artists offer something equally vital: a way of feeling through its mysteries. Geometry, in their hands, is both method and metaphor. Art can’t explain the universe. But it can make us feel it turning.
We begin with spirals and ellipses, forms that trace the deep structure of nature, from seashells to planetary orbits. These first two artists draw those curves into the body and the senses. From there, we move into tetrahedrons and tessellations: shapes of structure and repetition, where geometry becomes a ritual of building pattern and holding space. Finally, we arrive at networks and absence – not solid forms, but philosophies. These ideas allow us to reshape our understanding of meaning and our connection to the world. Buckle up, we're in for a few twists and turns.
The Spiral
Pathways through time
If we were to label the spiral as a geometric character in Galileo's "grand book", then it would be a cipher for time. It's ultimately nature's shrewd strategy of biding its time in the most efficient way possible before inevitable decay (or in scientific terms, the inevitable disorder of mass defined by the Second Law of Thermodynamics – known as entropy).
At the risk of sounding too clinical, let's explore this in the real. Take, for example, the velvety heart of a sunflower. It's seeds are packed into curling clockwise and counter-clockwise forms – spirals within spirals – nested forms that follow successive Fibonacci numbers, which visually equate to spirals. Essentially, nature does this for order: the seeds are packed in spirals to feel light, air and space in the most intricate, efficient manner.
And yet, the sunflower will eventually decay. The seeds will drop, and so the spiral will unfurl – as every living thing must eventually do. The same goes for pinecones, DNA strands, nautilus shells, whirlpools, galaxies. The list is near-infinite. All are formed as spirals to gather strength and maintain order whilst weathering the stormy inevitability of eventual decay. In this way, the spiral as an essential means of contemplating change itself. It's nature’s scaffolding before the fall.
Perhaps this pull towards life is why the spiral recurs so persistently in the human imagination too. The ancient Nazca people traced it across the desert plains, their geoglyphs visible only from the sky. Across continents and centuries, its form has been used to measure symmetry and beauty in temples, architecture, and painting. It appears in Hindu cosmology, Māori carvings, and Celtic stonework. Always circling, always returning. A visual chant of eternity.
"If something is in me which can be called religious then it is the unbounded admiration for the structure of the world"
Conceptual artist Alicja Kwade plays with the spiral’s symbolism in contemporary terms. In her 2012 installation Die Gesamtheit aller Orte (The Totality of All Places), she arranges 54 everyday objects — metal sheets, bent pipes, a door, a two-euro coin — in concentric rings across the gallery floor.
In the white-cube space, these objects become ritualistic. Modern doors sit alongside rusted Victorian-era gates. A bicycle beside a sheet of glass. The effect is temporal convergence: past and present folding inward. Each doorway suggests infinite trajectories. Time becomes a loop rather than a line.
Even the arrangement is fleeting. The gallery will clear; another artist will take its place. Kwade’s spiral, though poised, is only ever rented time. Her work makes entropy visible — not as a looming collapse, but as a condition already in play. Still forming, already rusting.
Ellipses
It's all about balance
We are bound by the rhythms of nature: the tilt of the sun, the glint of the moon, the silent tug of gravitational pull. These cosmic cycles have shaped human perception since the earliest civilisations, guiding technologies from calendars to agricultural rituals. One of the oldest surviving examples is the Goseck Circle in Germany. At first glance, this rickety assemblage of earth and wood appears elementary. In reality, it was a careful rendering of timber rings and gates to align with the sun's shadow so that sunrise and sunset would fall directly on its openings.
Its form, however, is not a perfect circle. And this is significant. It wasn’t until millennia later, in 1601, that the German astronomer Johannes Kepler reshaped our understanding of planetary motion. Planets, he discovered, do not orbit in perfect circles but in ellipses (elongated curves with two focal points). This revelation, the first of Kepler’s three laws, overturned the ancient belief in divine circular perfection. The cosmos, it turned out, was off-centre, asymmetrical, alive with motion and imbalance.
If ellipses were a character in Galileo's grand book of the universe it would be a signatory for cosmic balance. Here's why: inertia keeps objects moving in straight lines; gravity draws them inward toward mass. Between these opposing forces emerges the ellipse – a continuous curve suspended between escape and collapse, like a cosmic waltz. This geometry is felt everywhere: from the flittering of the sun across the sky to the ebb and flow of the tides. And we, glued by gravity to Earth’s surface, hurtle through space, are swept within this dance of space-time.
To feel this dance in an embodied way, step into Antony McCall’s Solid Light works. In darkened gallery spaces, McCall reduces light to misted beams; lines, cones, slow-turning arcs. The artwork title heralds from McCall's experimental play on solidity: any density in the light is only made visible by breath, smoke and dust conjured by the viewer's presence. The viewer's own body completes the circuit, revealing the form. As in Kepler's insight, McCall shows that perception and presence are part of the system. We must stand within the structure to truly see it.
As the viewer moves, these projections distort, collapse, reconfigure. The room becomes a coordinate system; bodies become variables. What appears to be light sculpture is, in fact, a study in relational geometry — a shifting model of spacetime that reveals how form is never fixed, but dependant on position and movement. In McCall’s installation, geometry is not abstract but a lived event, unfolding moment to moment through embodied perception.
Tetrahedrons
The Most Stable Shape of All
The tetrahedron is the most stable structure in the universe: four triangular faces locked in perfect symmetry. It’s rigid, efficient, impossible to collapse. As a shape, it underpins much of the world—from the water molecule (and therefore two-thirds of Earth’s surface) to the pyramids of Giza, whose geometry was designed not just to endure millennia, but to align earth and sky with crystalline clarity.
This intrinsic stability has made the tetrahedron a cornerstone of engineering and design, used in the construction of towers and bridges where strength is paramount. It also exists more subtly in nature. In chemistry, tetrahedrons define the spatial structure of molecules. Silicon dioxide (SiO₂), the substance that forms quartz, arranges itself in tetrahedral units. It is, geometrically speaking, the minimum number of points needed to enclose three-dimensional space. Nothing wasted. Nothing uncertain. Pure, structural minimalism.
And yet, the tetrahedron carries with it a curious contradiction. Plato, writing 2,400 years ago, believed it to be the elemental shape of fire. Among his five perfect solids—the cube (earth), icosahedron (water), octahedron (air), and dodecahedron (the cosmos)—the tetrahedron was the most volatile. With its sharp edges and lean geometry, it stood for transformation: fire as both destruction and possibility. A shape of perfect order representing the most unruly force.
It’s precisely this tension that British artist Conrad Shawcross investigates. He takes the most mathematically stable form and renders it unstable: stacking it, twisting it, watching it split, flower and buckle. Sometimes, he exposes its latent contradictions – like how tetrahedrons, despite their symmetry, cannot tessellate. They refuse to lock into a perfect whole. What should be a monument to certainty becomes, in Shawcross’s hands, a question.
By injecting motion into the most minimal of shapes, Shawcross rekindles Plato’s elemental vision of the tetrahedron: fire not as destruction, but as the engine of change. His forms spin, unfurl, collapse – leaving us dizzy, as though we’ve wandered into Alice’s dreamworld of falling logic and tilting forms. And this, it seems, is the point. Shawcross’s geometries remind us that even the most rational structures, when re-examined and unscrewed, become portals to new ways of seeing.
Geometry of Tesselations
How to reach Infinity
If Shawcross is playing with the fact that the tetrahedron cannot tesselate, then let's look at what it can feel like when something does. One of geometry's most elegant expressions is the tessellation: a repeating pattern of interlocking shapes, infinitely extendable. Take a polygon, like square or a hexagon, and place another beside it, edge to edge. Add another, and another. The result is a seamless configuration, a kind of puzzle that never ends.
Tessellations appear across cultures as practical design: their tight, gapless logic makes them ideal for tiling surfaces, both for aesthetical purposes but also because they allow water and dust to be easily wiped away. Behind this function though, tessellations carry deep symbolic weight. From Sumerian brickwork to Egyptian friezes, they have long signalled order and cosmic continuity. By the Islamic Golden Age (8th c.), tessellation became a metaphysical proposition: something infinite, perfect, harmonious — a symbol of God.
Inside the Shah Cheragh Mosque in Isfahan, Iran, that idea ignites into light. Much of this 14th-century sanctuary is coated in tessellated mirrorwork, each shard cut to precise angles, reflecting and refracting the smallest flicker of sunlight. The effect is dazzling: a choreography between order and dissolution, logic and radiance.
“It was a universe unto itself, architecture transformed into performance, all movement and fluid light, all solids fractured and dissolved in brilliance in space, in prayer.”
— Monir, 2008
When Iranian artist Monir Shahroudy Farmanfarmaian stepped inside the mosque for the first time, she later recalled it felt like “walking into a diamond at the centre of the sun”. This enixplicable encounter arguably shaped Monir's entire artistic vision.
Monir took the idea that geometry could contain the divine – or at least brush against it – and refracted it through a new language. Moving between Tehran and New York in the 1960s, she absorbed the rigor of Minimalism and the cool precision of Modernism. But unlike many of her contemporaries, who sought purity through reduction, Monir leaned into complexity. She returned to the tessellations of her childhood as a way to build a new artistic language.
Using āina-kāri, the traditional Iranian technique of mirror mosaic (long dominated by male craftsmen), she assembled sculptures and wall pieces that appeared both ancient and futuristic. In works like Nonagon (2011) or Untitled (Muqarnas) (2019), tesselating geometry becomes both object and encounter. As viewer looks in they are mirrored, multiplied, made part of the pattern. The sacred is no longer suspended above you in a vaulted ceiling. It’s brought eye to eye, inviting reflection in the most literal and conceptual sense.
When we see our face, our body, even our clothes reflected in the artwork’s glazing shapes, the act of looking shifts. It becomes more soulful, more entangled. You are not just observing the work — you are in it. Repetition becomes not just an aesthetic choice but an existential one. It asks: can we, like tessellations, unfold endlessly in all directions? Can geometry be not just a tool of measurement, but of becoming?
Networks
The Web Behind Everything
Speaking of infinity, let us consider how we too are part of a network that is perpetually growing. The desier to grow - to network - is present in the world itself: in silken roots fanning beneath a forest floor, migratory birds tracing invisible highways across continents. This impulse is ancient. We too mirror this pattern with our own hands: the Sajama Lines show pathways of connection over 2,000 years ago, paths to water, communities, towards pilgrimages. In contemporary times we see it in railways, flight paths, telephone wires, the internet. Even every thought, action, hope and dream is shaped by neural networks inside the brain. A geometry of connection weaves through everything.
At a philosophical level, the network is a model of being. Gilles Deleuze and Félix Guattari famously described life as a rhizome – a form of growth that spreads horizontally, erratically, with no clear centre or end. “Always in the middle, between things, interbeing, intermezzo,” they wrote. The rhizome defies hierarchy or fixed direction. Like a network, it proposes a reality shaped by relations, not by roots or rulers. This geometry invites us to think of life not as a linear path, but as a shared field of becoming.
This instinct to map belonging also runs potently through the work of Argentinian-born, Berlin-based artist Tomás Saraceno. For over two decades, he has worked across disciplines – collaborating with astrophysicists, engineers, philosophers and even spiders (who populate his studio at times) – to explore web-making as both structure and symbol. His research traces the geometric and symbolic principles that govern networks, from the cosmic to the gossamer, including the shared impulse among living beings to connect, organise, and relate. From this foundation, Saraceno builds ecosystems that emphasise the intricate webs that hold life together: tensile and reactive.
We see this logic fully realised in his installation In Orbit (2013–2024), where visitors ascend into a suspended web of steel mesh, suspended high in the glass cupola above the museum floor. As they move, the entire structure reverberates – each body affecting the whole. The artwork behaves like Deleuze and Guattari's rhizome in the physical: every movement has the capacity to change another's experience, all is interconnected, and all is influx.
This philosophy asks us to remember that we are all connected. When we zoom out – to the largest scale we can – we find the cosmos is woven in much the same way. In 1985, scientists discovered that the universe forms a vast cosmic web. Made largely from dark matter, it spreads and weaves a ghostly loom, binding the universe together. Planets and galaxies gather in dense pockets like dew on a spider web, echoing the same organising principles found in our everyday: spider webs, root systems and social networks. The structure itself is constantly growing and shifting – always becoming.
Left: Spider/Web Pavilion, 2010–2018
Right: Galaxies Forming along Filaments, like Droplets along the Strands of a Spider’s Web, 2008
Geometry of Absence
At the edge of Saudi Arabia’s Tayma Oasis, the Al Naslaa Rock stands improbably cleaved in two, its faces sliced with the clean, mathematical precision of a laser. Yet it is entirely natural. There is something compelling in the weightless space it creates between. Here, absence becomes form. Geometry is not only the outline of things, but the architecture of what is missing.
In every shape, there is a hollow – a negative space that gives structure to the whole. Absence is not a gap, but a generative principle. It shapes the shape. This kind of philosophy challenges us to remember that there is always a capacity for change, for becoming. In the end, all the geometry we have studies acts as varying principles for approaching the way we choose to see the world. Structure and symbolism — form and becoming.
It is this tension between presence and disappearance that drives the work of British artist Anish Kapoor. Throughout his career, he has pushed sculpture beyond the solidity of matter to explore the edge of reason. His early pigment pieces hovered between form and mirage. Later, in works like Descent into Limbo (1992) and Descension (2014), he carved into the world itself – vast voids that draw you in, physically and psychologically.
With Vantablack – a pigment that absorbs 99.965% of visible light – Kapoor made objects that cannot properly be seen at all. They do not reflect back; they absorb entirely, offering no return. This makes the work incredibly seductive. It's hard to walk away from a pit that gives you nothing: no light, no end, no certainty. This might be Minimalism pushed to its existential limit: an object so empty the viewer inevitably falls inward, watching thoughts and fears unspool into the dark. If no object is visible, what comes up for you?
“We shape clay into a pot, but it is the emptiness inside that holds whatever we want.”
— Tao Te Ching verse 11
Whatever you may wish to lie there, in absence is a place of potential. This is the primary focus of so many Eastern reigions: Buddhism's śūnyatā, Taoism's wu wei. Such ancient philosophies embrace the paradox that from absence arises the potential for transformation. In emptiness there is room for becoming.
Conclusion
Geometry is a multifaceted jewel, each face revealing a new perspective. In this essay, we’ve touched on only a few of its many dimensions, from the spirals found in nature and the ellipses that shape galaxies, to the intentional use of geometric forms in design. Tetrahedrons offer crystalline strength, tessellations speak to infinite repetition and beauty, and abstract networks hint at deeper meanings. Even absence and negative space become part of the language. Geometry challenges us to see not just what is, but what could be – encouraging a more connected, thoughtful way of understanding the world.
As William Blake wrote, “To see a world in a grain of sand, and a heaven in a wild flower… to hold infinity in the palm of your hand, and eternity in an hour.” This is what geometry offers – a glimpse of the infinite folded into the everyday.
If the journey has felt like ascending a staircase in low light – at times disorienting, abstract, or strange – know that this, too, is part of the geometry. Each step recalibrates your sense of space. What first felt intangible begins to take shape. Geometry isn’t something distant or academic. It is the ground beneath us, and the structure we rise through. It is how we build meaning, and how we can find our way home.
Calypso Lyhne-Gold
Curator, Research & Editorial
With a First-Class Degree in History of Art from the University of Bristol, Calypso is a rigorous researcher with a passion for supporting emerging contemporary artists. She has written extensively for Artelier and leading galleries, combining research with a keen understanding of global artistic trends and a rigorous approach to art market analysis.