Art in the Spirit of Geometry
- calypsolg9
- 9 hours ago
- 14 min read
This review explores the building blocks that make up our world. It follows the practice of 6 contemporary artists that illuminate essential geometric forces as visible, intimate and dazzling encounters.
Index of Artists: click on an artist to jump to their section.
What is Geometry? Why does it matter?
At its root, 'geometry' means 'to measure the earth'. It is one of humanity’s oldest methods of understanding the world, built by generations of mathematicians, scientists, and philosophers layering knowledge over knowledge. Geometry has been the foundation upon which civilisations rose and prospered. Today, we inherit a vast body of insight, and with it, the privilege to glimpse the intricate, marvellous structures that shape the world in which we live.
Long before it became a system of theorems and proofs, geometry served as a way of reading the world. Ancient architects aligned temples with the stars; farmers sowed crops by lunar rhythms; artists carved patterns echoing rivers, shells, and galaxies. It was understood intuitively, as a sacred conversation between form and meaning. Modern science narrowed this vision, rationalising geometry into a language of measurement and certainty. However, at its core, it remained what it had always been: a bridge between the seen and unseen, the tangible and the infinite. How does a tree branch? Why does the Earth orbit the sun? How do these laws shape us?
The following review traces how geometry continues to run through art and nature, not as cold logic but as a profound language of connection. It explores contemporary artists who, like the ancient makers, reimagine geometry not as clinical abstraction but as a living system — restoring wonder at the intricate architectures of existence.
Networks
The Web Behind Everything
Whether it’s the silken roots beneath a forest floor, fanning towards each other to share nutrients and messages across soil and seasons, or migratory birds tracing invisible highways across continents — the desire for connection is ancient. Across millennia, we have mirrored these patterns with our own hands: 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.
One of the earliest and most extraordinary examples of man-made networks is the Sajama Lines, often called “the largest artwork in the world”. Etched into the cracked skin of the Bolivian Altiplano by the Indigenous Aymara people over 2,000 years ago, these vast pathways span 16,000 kilometres. They were made by scratching away at the dark, oxidised earth to reveal the pale soil beneath, creating almost impossibly straight lines across the landscape. Whilst their literal purpose remains uncertain (some believe they marked pilgrimage routes, others that they guided communities toward water), their meaning transcends practical use. Ultimately, they present the instinct for life to create connective tissue: a way of situating oneself within something greater.
This instinct to map belonging runs 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, impulsive, 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 a living system, echoing the ancient lines that ripple across the Bolivian plateau or across roads and flightpaths. The gesture is the same: to map relation. We are all connected.
We really are. 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 same geometry beneath our feet reappears in the sky: lines drawn across dimensions.
Saraceno’s work inhabits this vertiginous scale-shift. In his solar-powered flight experiments and cloud-dwelling utopias, he invites us to see networks not simply as technologies but part of the fabric of existence; a way to tether ourselves to the world and, just maybe, to one another.
Left: Spider/Web Pavilion, 2010–2018
Right: Galaxies Forming along Filaments, like Droplets along the Strands of a Spider’s Web, 2008
The Spiral
Pathways through time
For many cultures, nature’s geometry is sacred. And one symbol, above all, whirs through time and across continents: the spiral. At once infinite and intimate, it has appeared in mythologies and landscapes from the Nazca Desert to Newgrange, from Hindu cosmology to Maori carvings symbolising ancestry, connection, and endless return.
The Nazca people of ancient Peru carved vast spirals into the desert floor; lines so immense they can only be seen from the sky, as if intended for gods or birds. Their purpose remains mysterious, but the devotion is undeniable: a land parched of water offering up the symbol of flow. Archaeologists have traced these paths and found them impossibly careful — so fine and deliberate that walkers would have moved single-file, tracing each loop like a slow, living prayer.
Yet the spiral is not just symbolic — it is a structural strategy that nature uses, again and again, to sustain life against inevitable decay. Growth demands it. To resist entropy — the slow unraveling of all things — nature organises with extraordinary efficiency. The Fibonacci spiral, seen in the heart of a sunflower, arranges seeds to give each the maximum share of light and space. In seashells, hurricanes, galaxies, the spiral reappears: a structure for gathering energy, holding tension, delaying the inevitable. The sunflower wilts, the shell cracks, cyclones lose momentum; all matter scatters eventually. But the spiral buys time — a brief architecture against the universal pull toward disorder.
"If something is in me which can be called religious then it is the unbounded admiration for the structure of the world"
This dance between structure and collapse, between the known and the unknowable, unfurls through the work of Alicja Kwade. In her 2012 installation Die Gesamtheit aller Orte (The Totality of All Places), 54 everyday objects — metal sheets, bent pipes, a door, a bicycle, a two-euro coin — are arranged in concentric rings across the gallery floor. Visitors walk each orbit like planets circling an invisible sun. From above, these familiar items seem caught in a spiralling drift, bound by some unseen gravity. As one critic put it, the installation feels like "a found-object bizarro-world solar system, a Berlin-bohemian crop circle or labyrinth" — an alternate cosmos where the everyday is made mythical.
Similarly, in her video Kreisel (Inception) (2012), a heavy metal top spins endlessly on a black stage, caught in perpetual motion. It never slows enough to topple, keeping us suspended in the loop. Here, there is no clear message, it's up to you. What is clear though, is that Kwade’s installations form coherent systems always on the verge of collapse: recalling how geometry and entropy are inseparable. By entrusting everyday materials with the languages of physics and chance, she draws us into a philosophical meditation: that reality is less fixed than it appears, an intricate game of perspective, pull and uncertainty. Time, for Kwade, is held in delicate equilibrium — forever turning, forever unravelling.
Tetrahedrons
The Most Stable Shape of All
The tetrahedron (also called a pyramid) is the most stable structure in the universe: four triangular faces locked in perfect symmetry. Rigid, efficient, impossible to collapse. For this reason, it has become a cornerstone of engineering, used to build towers and bridges where stability is paramount. In chemistry, it defines the basic structure of molecules. It’s also the minimum number of points needed to enclose three-dimensional space. Ultimately, the tetrahedron is pure minimalism, with nothing extraneous, nothing uncertain.
And yet, Plato assigned this most stable shape to fire: the most volatile, transformative element. Among the five Platonic solids — the geometries he believed formed the basis of everything — earth was the cube (solid, grounded), water the icosahedron (fluid, adaptable), air the octahedron (balanced). Fire, with its sharp edges and lean geometry, was the tetrahedron: stable, yet restless. It holds its weight but also suggests motion, thrust, ignition. This is the paradox at its core: the tetrahedron is both blueprint and blaze, structure and spark.
It’s precisely this tension that British artist Conrad Shawcross seizes on. He takes the most mathematically perfect form and makes it unstable: stacking it, twisting it, watching it split, flower, and buckle. Sometimes, he reveals its innate incongruity; such as how tetrahedrons, for all their stability, cannot tessellate, cannot lock together into a perfect whole. What should be a monument to certainty becomes, in Shawcross’s hands, a question.
There’s something quietly subversive about that. Geometry (especially tetrahedrons) is usually the language of control: blueprints, models, grids. Shawcross uses it to unmoor. In Paradigm, the tetrahedron explodes outward instead, in a radical inversion of its basic use.
Meanwhile, in Fraction (9:8) and Slow Arc Inside a Cube IV, modular tetrahedrons are assembled into kinetic machines that seem like they might solve something — but what, exactly, isn't clear.
By injecting motion into the most minimal shape, Shawcross rekindles Plato’s symbolic vision of the tetrahedron: fire not as destruction, but as the engine of change. His tetrahedrons spin, unfurl, collapse, leaving us dizzy, as if we've stumbled into Alice’s underworld. This, it seems, is precisely the point. Shawcross’s geometries remind us that even the most rational structures, when reexamined and unscrewed, can open portals to new ways of seeing.
Circles & Ellipses
How the circle bends to keep everything in balance
At first glance, the Goseck Circle appears as a simple ring of earth and wood. In reality, it was one of humanity’s earliest attempts to track the sun. The timber ring and gates align so precisely that, for example, the winter solstice sunrise and sunset fall directly along the southern openings. Although circular in plan, and not a true mathematical ellipse, Goseck was an early attempt to ground the rhythms of the sun and moon in earthly architecture.
Millennia later, that intuition became scientific law. In 1601, German astronomer Johannes Kepler published a discovery that would forever reshape humanity’s understanding of the cosmos: planets do not move in perfect circles, but in elliptical orbits. Gravity pulls them inward, while inertia is a force moving matter in a straight line unless acted upon by something external. If inertia were the only force, a planet would travel straight forever. The intricate interplay of these forces creates a curving path — a cosmic waltz — the same slow drift that the builders of Goseck sought to mark, now revealed in precise mathematical elegance.
This elliptical dance 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, planes, slow-turning arcs. The ‘solid’ shapes — conjured from breath, smoke and dust — are not fixed objects but momentary architectures, shaped by the viewer’s presence. You too drawn in, the artwork snaps you into awareness. Caught in the projection, each one curls into form, all matter within the light — the artwork itself — is in constant flux, never the same. Much like our solar system: ever-changing, evolving, and yet held together by enduring laws. It’s a perfect microcosm to contemplate greater laws.
There is something deeply elemental about this. McCall did, in fact, emerge from the Minimalism movement. But his installations stand in stark contrast to the rigid, hard-edged works of an iconoclastic minimalist like Donald Judd. Instead, by nature of them being performative they requiring an audience to activate the artwork. This, along with the nature of light as a material, makes his Solid Light feel gauzy, ephemeral — as though the viewer is hovering between two realms: one governed by the clean mathematics that define us, and the other by the trembling, tangible world itself.
Geometry of Tesselations
How to reach Infinity
Take a polygon, like a hexagon or square. Place another next to it, matching one side to another. Add another, and another. You now have a tessellation: a pattern of shapes that fit perfectly together, capable of repeating forever, infinitely.
Because of their practical and aesthetic power to create infinite pattern, tessellations have fascinated artists and architects across civilisations. The Sumerians used them in decorative brickwork and mosaics to impose order; the ancient Egyptians adapted repeating motifs — lotus flowers, grids — as symbols of renewal and eternity. By the Islamic Golden Age of the 8th century CE, tessellation reached dazzling new heights: geometry became a language to express the infinite nature of God, perfected in architecture, ceramics, and manuscripts. And what happens when you make tessellations from mirrors? Light itself becomes infinite: multiplied, fragmented, always shifting and ultimately refracted into boundlessness.
Nowhere is this more breathtaking than at the Shah Cheragh Mosque in Isfahan’s central square, a towering UNESCO World Heritage site where every surface is covered in glittering tessellations. Its name, "Shah Cheragh" (meaning King of Light), comes from a legend: a 14th-century queen commissioned mirrorwork to magnify the sun’s rays; she wanted a temple that could reflect God's magnificene like a blazing, awe-inspiring light. The interlocking designs are central to this effect, with each shape coaxing the reflections into a varied yet harmonious orchestra. A glimpse of the infinite, anchored in logic. What better way to describe God?
It is no surprise that when Iranian artist Monir Shahroudy Farmanfarmaian first walked into the mosque, she likened it to "walking into a diamond at the centre of the sun". Sublime light, glimmering possibilities: this enixplicable encounter arguably shaped Monir's entire artistic vision.
“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
Even after she moved into the glitterati of 1960s New York, the memory of that luminous mosque remained a lodestar. Amidst the minimalist grids and pop exuberance of the era, Monir cut through to the bare essentials: reordering the tessellating geometries of her childhood into a new language aligned with the cool-cut vernacular of Modernism, particularly with the hard-edged Minimalists of the 1960s who reacted against the painterly excess of Abstract Expressionism. Monir was the first artist to achieve a practice that wedded geometric patterns with Iranian cut-glass mosaic techniques (Āina-kāri): a tradition previously reserved for men.
And where Minimalism sought to reduce distraction to achieve bliss through simplicity, this is where Monir's work shines. Her practice distils deeply significant and complex sacred geometric forms into crystalline, meditative objects reflecting the everyday: the changing light, the bustling exterior, the shifting self. Infinity is made personal. In Untitled (Muqarnas) (2019), the age-old Islamic muqarna is pulled down from the vaulted halls of the mosque to meet the viewer face to face; look closely, and you too are dispersed into endlessness as your reflection scatters across a mirrored tessellating surface. In Convertible Series (2010-2019), she pushes the idea even further: modular, mirrored objects that tessellate physically, designed to interlock and unfold endlessly. Each sculpture can be shaped and reshaped according to the viewer’s sensibility, making the experience of infinity not only visual but participatory. A shimmering encounter with infinity itself.
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. A spiral curls around an unseen axis. A tetrahedron holds a crystalline cavity at its core. Geometry is never just mass — it is the balance of volume and vacuum, edge and emptiness. Absence is not a gap, but a generative principle. It shapes the shape.
It is this tension between presence and disappearance that drives the work of British artist Anish Kapoor. Throughout his career, Kapoor 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. Perhaps this is Minimalism pushed to its ultimate edge: a space 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 relligions: Budhhism's sunyata, 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
It’s been a whirlwind. On one level, we’ve identified the foundations of our existence, both literally and symbolically. And on another, we’ve peered through the looking glass anew. It becomes inescapable: once you study geometry, you begin to witness something more primordial than civilisation itself — a language older than words. Mathematics is a philosophy and art form in its own right. It can be complex, but it is also simple.
In an era when the pace of life fractures our sense of belonging, reflecting on these hidden structures can bring moments of bliss. This might come through artworks that flirt with geometric systems or through the delicate filaments etched into a leaf. Either way, the universe’s ancient inheritance is written and rewritten everywhere: in the veins of rivers, the rise of mountains, the heart of a sunflower. 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.”
And when we feel as though we’re spiralling — fractured, existential, or lost in an endless ascent through ideas — it’s important to return to solid ground. When you do, you may realise that the steps you climbed were home all along. Geometry is not separate from us. It is the bedrock of our existence. From the tiles on a bathroom wall to the floorboards beneath our feet, geometry is the unseen staircase we move along every day.
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.
