George Balanchine's statement "See the music, hear the dance" is often quoted as a way of appreciating the architecture of his choreography, manifested from the score. The mathematics of music transmutes into movement in the flesh.
But we often take for granted the geometric shapes that comprise ballet's architecture and what they represent. It seems there exists a sort of sacred geometry, universal principles informing these configurations that penetrate the subconscious. The symbolic meanings inherent within these harmonic shapes found in nature subsequently take ballet—as well as painting, architecture and other arts—into a deeper world of elucidation.
Take the second act of Swan Lake, for example. Shortly after the swan corps enters, they form a formidable triangle, aimed like a spear towards the audience, that defines the power of the flock. They then form circles around Siegfried in unity of their sisterhood. These shapes are not random formations—they embody the music's emotional and energetic charge. When you see a triangle in nature, say, a mountain or a tree, there is a clear sense of groundedness from the base to its apex, a divine clue of where the energy is heading. Geometry carries intention.
It's easy to see how the spatial awareness and the eight positions of the body in ballet, governed by a square, establish a foundational vocabulary, with the spine as the midline. The shapes that flow from that base speak their own language. The acute angle of a polite tendu in effacé differs from the oblique angle of a forceful battement croisé.
In Act II of Giselle, the wilis form four parallel lines of traveling arabesques that register as a force of nature. In one of the ballet's most potent visual images, they part to the sides of the stage to yield to Myrtha, who slices the stage with a fierce diagonal of jetés. To unwaveringly validate her regal power, she completes a spacious circle of sauts de basque, circumscribing her domain at the intersection of the afterlife and karmic payback.
When Margot Fonteyn piquéd into an ideal first arabesque as Aurora in 1946, she formed a perfect right angle, as if to say "All is right with the world." Like Aurora vanquishing Carabosse, Great Britain witnessed a new dawn, and her perfect arabesque could be seen as symbolizing the nation's triumph over Nazi forces.
In the Sleeping Beauty vision scene, the Lilac Fairy directs the Prince as he pursues Aurora's apparition. They weave in and around two diagonal lines of the corps, like a DNA helix that might rewire human progress.
At the conclusion of the third theme pas de deux in Balanchine's The Four Temperaments, the ballerina, facing away from her partner, takes slow, sweeping ronds de jambe. As they exit on the final chord, she extends her legs forward, parallel to the floor, reaching into the wings as if pointing the way to the truth about our temperaments.
Anyone who has seen Jerome Robbins' Glass Pieces sees that kaleidoscope of shifting geometry as a metaphor: All of life is geometry, moving from one shape to another.
And even the dizzying spiral of those ubiquitous 32 fouettés reveal the triumph, joy or dominance of the spinning heroine.
Rudolf Laban, whose work led to Labanotation, a codified system of recording choreography, was inspired by the mathematical and spiritual theories of Plato and Pythagoras. He forged his philosophy of "space harmony": spatial exercises linked to musical scales (with their own mathematical system), which flow through the structures of geometric shapes, such as the cube and the octahedron. He linked complex mathematical sequences, like the proportions of the golden ratio (phi), used by painters like Michelangelo and architects like Ludwig Mies van der Rohe, to movement and its relationship to human body proportions.
Choreographer William Forsythe, known for expanding the dimensions of ballet, and influenced by Laban's principles, created a series of videos called Improvisation Technologies, demonstrating sequences like "shearing space" and "following a curve to its logical conclusion."
"Our body is the mirror through which we become aware of the ever-circling motions of the universe with their polygonal rhythms," Laban wrote in his book Choreutics.
Laban also spoke of the kinesphere, the spatial sphere that surrounds the human body into which its limbs reach. Leonardo da Vinci illustrated the natural geometric configurations of the human body in his drawing of the Vitruvian Man, depicting a male figure with his arms and legs outstretched, surrounded by both a circle and square. The navel is the center of the body and his extended limbs define the circumference of the circle. (The School of American Ballet once used Vitruvian Man as a logo in its marketing.) The symmetry of the body with its idealized proportions is quite striking.
Modern dance also uses geometric concepts, as seen in Merce Cunningham's richly abstract shapes and his embrace of negative space. Or witness the articulation of a Martha Graham spiral sequence. But ballet's strict symmetry makes its commitment to geometry even more evident.
In fact, scientific research has found that evolution has led us to favor symmetry in nature. In "The Science of Art: A Neurological Theory of Aesthetic Experience," the authors V.S. Ramachandran and William Hirstein propose that the visual processing of symmetry and core object recognition develop early in maturation and over time have served as an early detector for spotting prey and for choosing a mate. Evolutionary biologists have proposed that asymmetry in nature is linked in our brains to infection and disease, so the aesthetic preference for symmetry is hardwired. (This is not to say that asymmetry isn't aesthetic in art or nature. It's just that the brain generally recognizes symmetry as organically pleasing.)
A relatively new field of science has emerged called "neuroaesthetics," initiated by the research of neuroscientists V.S. Ramachandran and Semir Zeki. Neuroaesthetics explores the connection of brain sciences and our response to aesthetic experiences in the arts, whether by gazing at the Taj Mahal or watching the finale of Symphony in C. Via the optic tract, the brain implements core structure recognition to define the geometry of a space. The bioarchitect Michael Rice says these patterns can present pleasant images to our subconscious that trigger the brain's reward system to release chemicals, like dopamine and serotonin, that produce pleasurable sensations and positive emotions.
But beyond the visual gratification of perceiving geometric formations also lies their inherent symbology. Movement speaks its own language through form and patterns. So if sacred geometry finds symbolic meanings within nature's harmonic shapes, you can also find those in examples from ballets.
For many, it's natural to appreciate the aesthetic beauty and to intuit the subliminal profundity of ballet. Understanding the geometry behind it just enriches the experience.