Hannsjörg Voth’s Golden Spiral

Hannsjörg Voth's Golden Spiral Moracco
Hannsjörg Voth’s Golden Spiral Moracco

Art and mathematics may seem like two entirely different fields, but they have a lot in common. Mathematics lends itself to the laws guiding the natural world, while art evokes emotions and captures the beauty surrounding us. When both these fields come together, they create something truly exceptional, just like Hannsjörg Voth’s Golden Spiral.

Hannsjörg Voth’s Golden Spiral is an ode to the Moroccan desert’s majestic beauty, and his inspired use of mathematics in these large-scale projects is nothing short of awe-inspiring.

Hannsjörg Voth's Golden Spiral
Hannsjörg Voth’s Golden Spiral in the heart of the Moroccan desert.

Hannsjörg Voth’s Golden Spiral stands in the heart of the Moroccan desert, and its beauty takes your breath away. The structure has a series of nine-quarter circles arranged in an unusual sequence, but what sets it apart is how the radii increase. The radii increase is based on the Fibonacci sequence, where each number is the sum of the previous two. Voth’s inspired use of this sequence has intriguing implications – this sequence is a pattern present in many natural processes, from the branching of trees to the spiral shapes of shells.

Hannsjörg Voth's Spiral
If you want to see this pure art one day, here are the coordinates.

The Golden Spiral‘s radii increase following the Golden Section. This proportion divides a line segment into two parts so that the smaller-to-larger ratio is the same as the larger-to-the-whole ratio. This proportion also appears in many natural processes, from the proportions of human bodies to how seashells are formed. When you combine the two patterns, you see a structure that mimics both the natural world and mathematical law.

But, this is not the first time that math and art have intersected. They have a long, storied history where many artists have used mathematical principles in their artworks. One common example can be found in Islamic art, where intricately designed patterns employ the principles of geometry and often include tiling and tessellation.

Other artists who also blended mathematical laws, like Voth, include Rafael Lozano-Hemmer and Mercedes-Benz, to name a few. Rafael Lozano-Hemmer combined geometry and computer science to create interactive pieces like light sculptures like Cubatron For Pulse, which creates a polyhedron of light from 3,000 colored bulbs. Another example is when Mercedes-Benz used a “3D painting robot,” which employs trigonometry and calculus to create generative art on car parts.

Hannsjörg Voth's Golden Spiral Art
Hannsjörg Voth Goldene Spirale, 1994 at the Mercedes-Benz Art Collection

Art and mathematics are not as far apart as we might think. The intersection of these fields offers endless possibilities, and Hannsjörg Voth’s Golden Spiral is proof of that. Whether it’s Islamic art, Rafael Lozano-Hemmer’s interactive pieces, or the generative art by Mercedes-Benz, it’s inspiring to see how artists have used maths principles in their works. The fact that the principles of mathematics and natural law are being translated into art is a testament to how much these fields have in common.

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Ali Kaya


Ali Kaya

This is Ali. Bespectacled and mustachioed father, math blogger, and soccer player. I also do consult for global math and science startups.