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Tags: architecture | beauty | theory | math

The Beauty of Math in Architecture

The Beauty of Math in Architecture
Tourists enter the ancient Parthenon temple atop Acropolis hill in Athens on July 20, 2018. (Angelos Tzortzinis/AFP/Getty Images)

Alexandra York By Tuesday, 28 August 2018 02:55 PM EDT Current | Bio | Archive

Humans are hardwired to find delight in nature’s designs. We gravitate toward order rather than chaos. We like spirals, curves, zigzags, symmetry, harmonious proportion, and congruence: snail shells, waves, sunflowers, honeycombs, galaxies, leaves… all of nature’s fractal compositions that create an integration of details the whole of which seems so much greater than the sum of its parts. A fractal is a repeating geometric pattern that can be subdivided endlessly into parts, each part being a smaller copy of the whole; yet, it is the “finished” structural pattern that charms us.

How do nature’s geometrical pleasures transfer to manmade forms of architecture? Does an element of humanism enhance this art form to turn nature’s purely optical pleasure into a personal and/or communal one? As usual, we repair to ancient Greece for answers. Born from requirement to measure land — "geometry" means “earth measuring” — the Babylonians and Egyptians used geometry empirically to construct civic and religious buildings millennia before Greek flourishing in 5th-century BCE. But when Greeks eventually traveled to “modern” versions of those early civilizations, they not only learned much about math in general but also expanded the basics — geometry in particular — into a scientific philosophy that became a separate discipline.

Pythagoras (569 BCE) started it while visiting Egypt and grasping principles beneath brilliant but experientially achieved structures. Founded on these enduring principles, he created a complete system of mathematics where geometric elements could correspond with numbers and where whole numbers and their ratios could establish an entire system of logic and truth part of which is known as the Pythagorean Theorem. Duly influenced, Plato (428 BCE) saw geometry’s value by stating: “those arts which are founded on numbers, geometry and the other mathematical disciplines, have greatness and in this lies the dignity of architecture.” Mathematics as a stand-alone subject was thus firmly established.

Greek sculptors and architects put geometric knowledge into exquisite practice by incorporating the Golden Section — or Golden Ratio — method of mathematically ensuring balance and proportion in their creations, both qualities embracing natural and humanistic presence in abstract design. Sculptors imbued physical beauty and mental heroism into their perfectly (geometrically) proportioned figures, thereby integrating mind and body into a spiritual whole; Polyclitus (420 BCE) is famous for “The Doryphoros” (“Spear Thrower.”) Architects, by designing the most purely abstract manmade entities that display geometry’s essence, infused structures with humanism because a building’s physical form is (or should be) governed by utilitarian function in human life; hence, the dictum: Form follows function.

The iconic Parthenon (447-432 BCE) overtly honors humanistic values, not only those of its main statue of worship — Athena, Goddess of Wisdom —but also teeming with anthropological figures: gods and humans behaving together in one fashion or another (suggesting man’s equality with the gods) on its frieze. Among countless other features proclaiming the value of the individual, the columns were subtly adjusted in width to assure that from a distance they appeared straight and strong like a man should stand. It is believed that each column was another conscious metaphor for humanity in a more personal way, each column being six times its diameter in height because the average man’s foot was one-sixth of his height.

The only surviving ancient treatises on architecture that draws a connection between the human body and that of a building are found in ten books by Roman architect Marcus Vitruvius in approximately 20-30 BCE. He focused on three themes that must be inherent in a proper structure: fermatas (strength), utilitas (function), and venustas (beauty). In his famous image (more famously portrayed by Leonardo Da Vinci (1452)), he showed the ideally proportioned human body fitted precisely into both the circle and the square, illustrating the link between perfect geometric forms and the perfect body. Along with harmonious geometric proportions, beauty as a crucial feature of good design was also stressed by Renaissance architect Leon Battista Alberti (1404) who defined beauty as “that reasoned harmony of all the parts within a body, so that nothing may be added, taken away, or altered, but for the worse.”

All of the arts utilize math. Painting and sculpture necessitate an underlying geometric design to support composition. Fictive arts require thematic structure — a beginning, middle, and end — to support story progression. These arts indirectly address existential reality via representation of visual images and/or symbols (words) anchored in organization of form. In music, the notations of composers developing a theme and vibrations/frequencies emitted from instruments playing that theme are both connected to mathematics, e.g. intervals, patterns, harmonies, pitch, tempo, etc. and help communicate melodious sounds directly to listeners. Comparing music’s abstract sound vocabulary to architectural language, Deryck Cooke (“The Language of Music,” 1959) brilliantly analyses emotions expressed in music by saying music uses “tone” instead of “stone” as its communication channel.

Yet architecture stands alone in consisting of abstract, mathematically designed physical substances and forms as its only means of communicating. Communicating what today? Modern technology offers structural materials that support while seeming to defy gravity, meaning buildings can look as if toppling over or exploding in space. Some new, sleek buildings astound and astonish, but most exude either boxy-static, low-cost-driven sterility or the “Look-at-me!” subversive narcissism of architects. Beauty is out and banality or brutalism reigns. Why? Like all arts, architecture reflects its era. Ours is a time when life-affirming values of beauty, proportion, and harmony that support humanism are fading; dull or aesthetically offensive structures — both dehumanizing — are on the rise. Like other signs of cultural deterioration — distraction replacing contemplation, noise replacing music, freakishness replacing taste, violence replacing civility — architecture is in alarming disarray.

Perhaps we need the rigors, refinements, inherent beauty, and sanity of math to re-emerge in our manmade architectural landscape in the same way that the geometry of fractals remains in our natural surroundings. Perhaps we (and contemporary architects) need think on this.

Alexandra York is an author and founding president of the American Renaissance for the Twenty-first Century (ART) a New-York-City-based nonprofit educational arts and culture foundation (www.art-21.org). She has written for many publications, including "Reader’s Digest" and The New York Times. Her latest book is "Adamas." For more on Alexandra York, Go Here Now.

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Perhaps we need the rigors, refinements, inherent beauty, and sanity of math to re-emerge in our manmade architectural landscape in the same way that the geometry of fractals remains in our natural surroundings.
architecture, beauty, theory, math
Tuesday, 28 August 2018 02:55 PM
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