A simple formula that has been inspiring the world's most creative designers for centuries.
Designers actively shape their individuality and creative instincts through various influences, from conscious inspirations and references to more abstract and unknown sources. Over time, their creations — marked by evolving shapes and structures — push boundaries and deepen our understanding of how form and function can interact. One intriguing influence on design, spanning from historical figures like Leonardo da Vinci to modern innovators like Rohan Mirza (pictured above), is mathematics.
Mathematical principles, particularly those governing proportion and symmetry, have long inspired and guided designers. The golden ratio, also known as the Fibonacci Sequence, approximately 1.618, discovered by Leonardo Fibonacci in 1202, is one of the most enduring examples of this intersection between art and math. Often referred to as the golden number or golden proportion, it is a fundamental mathematical concept and a guiding principle for designers seeking to capture balance and harmony in their work. This principle informs the Fibonacci spiral, “the perfect spiral.” Based on the Fibonacci sequence, it’s a formula that can be used to create harmony and balance. Popular because it naturally occurs within nature examples include pinecones, hurricanes, and spiral galaxies. Its lasting presence in design blends several mediums with the natural world.
The Fibonacci spiral is based on the Fibonacci sequence, a series of numbers in which each number is the sum of the two preceding ones. For example, the sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. To visualize the Fibonacci spiral, you represent each number in the sequence as the side length of a square. You then arrange these squares in a counterclockwise pattern, positioning each new square adjacent to the previous one.
The growing spiral formed by connecting the corners of these squares resembles many natural forms, such as the spiral arrangement of sunflower seeds or the curve of a snail’s shell. A mathematic formula that can provide a sense of connectivity to the natural beauty of the world, the curve of a wave before is crashes, the curve of a seashell. However, the complexities of translating the Fibonacci spiral into wearable fashion and functional structures arise from its abstract mathematical nature. Designers must carefully manipulate fabric and other materials to maintain the proportions of the spiral while ensuring the garment remains functional and comfortable. This requires a deep understanding of both geometric principles and textile behavior, presenting a creative challenge to integrate the concept without compromising practicality.
This spiralling introduces a sense of movement and fluidity to designs by guiding the viewer’s eye along its naturally expanding curve. In fashion, when this spiral is applied to patterns, seams, or draping, it creates the illusion of continuous motion, as if the fabric is unfolding or growing organically around the body. This dynamic quality brings life and energy to garments, making them appear in motion even when the wearer is still. The flowing lines and asymmetrical designs mimic the spiral’s curvature, adding grace and a natural rhythm to structured forms. The formations grow and expand, creating a sense of seamless progression. By incorporating the golden ratio, designers tap into these natural rhythms, connecting their work to the organic world. In architecture, graphic design, and sculpture, this spiral similarly conveys a sense of growth and flow, transforming static forms into dynamic, living expressions of nature’s inherent order.
One of its most famous admirers was Leonardo da Vinci, who often incorporated the spiral into his works across various mediums. Many art historians believe that da Vinci utilized the golden ratio in his paintings, including the Mona Lisa. The theory suggests that people perceive objects or faces aligning with the golden ratio as more aesthetically pleasing. This is why many regard the Mona Lisa as one of the most beautiful and harmonious portraits of its time. This speaks to the connection the Fibonacci sequence can bridge between art and nature, creating a sense of natural beauty and harmony. He also extrapolated these mathematical principles in architecture, most notably in the design of the double-helix staircase at the Château de Chambord. Widely considered a masterpiece of French Renaissance architecture, consists of two intertwining spiral staircases that allow visitors to ascend and descend without crossing paths.
Leonardo da Vinci often explored these natural shapes and patterns in his work. The spiraling staircase, like da Vinci’s sketches of swirling water and growing plants, taps into the rhythms of the world around us. The spiral makes the staircase practical but also draws the eye upward, adding a sense of movement and grace, much like nature’s own designs. Da Vinci was fascinated by the underlying patterns and structures found in the natural world, often mimicking the ways in which nature organized itself in his own designs. His studies of water currents, plant growth, and human anatomy revealed his belief that nature operated through universal principles, which he sought to capture. By enclosing each staircase the other side was only visible through the small windows in the walls. Walking upward in the enclosed space DaVinci created, you are completely one with the architecture, completely one with nature.
In a modernist context, architect Bruce Goff designed the Bavinger House in Norman, Oklahoma, creating an award-winning structure renowned for its innovative use of the Fibonacci spiral. Goff, like many visionaries, was profoundly inspired by organic forms and the harmony found in nature. He designed the Bavinger House with a strong connection to natural forms, particularly the Fibonacci spiral. Goff’s approach to design often mirrored nature’s geometry, and in the Bavinger House, he used the golden ratio to create a structure that felt like a natural extension of the landscape. His attention to detail extended even to his preliminary sketches, where he meticulously drafted every aspect of the design. This design reinforced Goff’s commitment to organic architecture, which he described as integrating "the natural elements into the building rather than imposing the building upon them."
Central to the house’s design is a 96-foot-long spiral, inspired by the Fibonacci sequence and securely anchored to the ground using a recycled drill stem. The house’s spiraling roof, constructed of stone, seemed to grow out of the earth, reminiscent of the way plants unfurl towards the sun. Goff’s fascination with natural forms and materials is evident in the way he integrated irregularly shaped stones and glass into the walls, creating a dynamic interplay of light and texture that echoed the randomness found in nature. His design of suspended "pods" within the house, hanging in a spiral configuration, was not only functional but also symbolic of nature’s interconnectedness and continual growth.
The curve of the walls provided both visual continuity and structural integrity. By following the natural expansion of the spiral, the design allowed the space to unfold organically, creating a unique flow throughout the house. This not only enhanced the aesthetic appeal but also contributed to the building’s structural stability. The curved walls, arranged in accordance with the Fibonacci spiral, distributed weight evenly and created a sense of spatial harmony. The Bavinger House stands as a testament to this, evoking both the serenity and complexity of the natural world. You can read more in depth about the structure on our Archived Dreams Blog here.
The influence of the Fibonacci sequence and the golden ratio continues to captivate modern designers, and Rohan Mirza is a prime example of how these mathematical concepts can shape contemporary fashion. His work exemplifies how mathematical concepts, can extend beyond their theoretical roots to inspire dynamic, visually striking designs connecting to the wrold around and creating harmony. The earrings although visually striking and unique, could remind one of seashells, echoing this same connectivity. By embracing these principles, Mirza has developed a signature style that emphasizes the harmony and proportion that the golden ratio is renowned for, echoing the timeless appeal these ideas have held in art and design. Hence why designers alike have used the ratio as reference for so long throughout history.
The Fibonacci sequence and its related principles have sparked countless innovative and boundary-pushing creations over the centuries. The golden ratio, in particular, remains a source of fascination for artists and designers today, as it is associated with balance, harmony, and beauty. This mathematical approach to design connects the modern world to the age-old belief that beauty is inherently tied to the patterns of nature.
