As you rush to the nearest dining hall, you watch someone whip out their phone and snap a dramatic photo of Zeppos Tower. Maybe it was a tourist or maybe it was even you, uploading it to your Instagram story. But why are so many people constantly compelled to take a picture of a seemingly simple tower? Are we all subconsciously innate architects? In reality, our actions are driven by math — our affinity for symmetry, geometric balance, and proportional perfectness.
Math is all around us
Think back to the last time you held a seashell. Maybe you immediately thought about the precise biomineralization process of calcium carbonate crystallizing into aragonite, forming a logarithmic spiral following the Fibonacci sequence of this lavish shell. (If you didn’t, you undoubtedly will now.) The Fibonacci sequence is a string of numbers where each element is the sum of the two elements that precede it: 0, 1, 1, 2, 3, 5, 8, 13, and so on. The golden ratio, a number approximately equivalent to 1.618, is the value of the ratio between any two consecutive Fibonacci numbers. Written as Φ, the Greek symbol phi, the golden ratio is a mathematical concept ubiquitous in nature, appearing not only in the spirals of shells but also those of plants and solar space.
The golden ratio is believed to have been produced between 468 and 430 BC. Despite arguments about whether the golden ratio was invented or discovered, it is absolutely undeniable that it is present in some of the most fascinating buildings on Earth. The Chichen Itza pyramids in Yucatan, Mexico, as well as much of classical Greek architecture follow this intricate mathematical model. Today, modern architects and engineers intentionally integrate it into their designs for buildings. The Notre-Dame Cathedral, the Taj Mahal, and the Parthenon are some wonders today that contain proportions based on the golden ratio.
Just as the golden ratio exemplifies the harmony between mathematics and aesthetics in design, other mathematical constructs derived from nature have similarly inspired architectural innovation. In the early 1900s, Ukrainian mathematician Georgy Voronoi proposed a formal definition and framework for the partitioning of planes into regions we know today as Voronoi patterns. Picture the coat of a giraffe or the cracks of dry mud. These are both particular patterns known as Voronoi diagrams (Dirichlet tessellations). Voronoi patterns, according to the School of Mathematics from the University of Bristol, are “created by scattering points at random on a Euclidean [flat] plane.” The result is a network of tessellating (non-overlapping) polygonal regions that together cover the entire plane. They can be described as fractals — geometric shapes that infinitely repeat themselves at multiple scales.
In modern architecture, engineers and architects use parametric designs to create structural features based on algorithmic processes, some of which include Voronoi and the golden ratio abstracts. As such, Voronoi constructs have been adapted into buildings using these parametric designs to create organic and complex facades, exhibiting qualities of mathematical beauty.
The Collegiate Gothic architectural style at Vanderbilt
During a celebratory dinner in 2014, Chancellor Nicholas S. Zeppos revealed the grand plans for the university’s transformation of the residential colleges. Following traditional residential college models such as those of the University of Oxford and University of Cambridge, Vanderbilt University undertook a $600 million transformation project to offer 220,000 square feet of living for students. Designed by David M. Schwarz Architects and HASTINGS Architecture, these buildings reflect a delicate balance of geometric elegance and symmetrical balance, elements rooted in mathematical theory. The Collegiate Gothic style used in the residential colleges is no random choice but rather a deliberate product of engineering. It is perhaps for this very reason that students and visitors pause to admire Vanderbilt’s architecture, as its beauty is nothing but pure mathematical principles.
References
Angen, K. (2021, April 9). A gothic revival facade at Vanderbilt University “sprinkles” The past with modern efficiency. The Architect’s Newspaper. https://www.archpaper.com/2021/04/facades-vanderbilt-university-e-bronson-ingram-college/
Golden ratio: A beginner’s guide | adobe. (n.d.-a). https://www.adobe.com/creativecloud/design/discover/golden-ratio.html
Owens, A. M. D. (1970, February 11). “skyscraper gothic” opens at Vanderbilt Fine Arts Gallery. Vanderbilt University. https://news.vanderbilt.edu/2022/02/11/skycraper-gothic-opens-at-vanderbilt-fine-arts-gallery/
Vanderbilt University E. Bronson Ingram College: Hastings Architecture. Vanderbilt University E. Bronson Ingram College | HASTINGS Architecture. (n.d.). https://www.hastingsarchitecture.com/project/vanderbilt-university-e-bronson-ingram-college
What is a Voronoi diagram? | school of mathematics | university of Bristol. (n.d.-b). https://www.bristol.ac.uk/maths/fry-building/public-art-strategy/what-is-a-voronoi-diagram/
