Daring Diagonal Virtual Museum


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DiagonalityIn CertainNatural Sponges

In Certain
Natural Sponges

We think of marine sponges as soft and pliable, but some sponges actually have glassy skeletons. The skeletons are diagonally-reinforced square lattices. This diagonal reinforcement of the skeletal structure, according to researchers at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) “has a higher strength-to-weight ratio than the traditional lattice designs that have [been] used for centuries in the construction of buildings and bridges. …We found that the sponge’s diagonal reinforcement strategy achieves the highest buckling resistance for a given amount of material, which means that we can build stronger and more resilient structures by intelligently rearranging existing material within the structure,” said Matheus Fernandes, a graduate student at SEAS.

“In many fields, such as aerospace engineering, the strength-to-weight ratio of a structure is critically important,” said James Weaver, a Senior Scientist at SEAS. “This biologically-inspired geometry could provide a roadmap for designing lighter, stronger structures for a wide range of applications.”
Leah Burrows writes about this discovery in News and Events, published by SEAS. She writes: “If you’ve ever walked through a covered bridge or put together a metal storage shelf, you’ve seen diagonal lattice architectures. This type of design uses many small, closely spaced diagonal beams to evenly distribute applied loads. This geometry was patented in the early 1800s by the architect and civil engineer, Ithiel Town, who wanted a method to make sturdy bridges out of lightweight and cheap materials.”

Matheus Fernandes wrote “Town developed a simple, cost-effective way to stabilize square lattice structures, which is used to this very day. It gets the job done, but it’s not optimal, leading to wasted or redundant material and a cap on how tall we can build. One of the main questions driving this research was, can we make these structures more efficient from a material allocation perspective, ultimately using less material to achieve the same strength?”

Luckily, the glass sponges, the group to which Euplectella aspergillum — otherwise known as Venus’ Flower Basket belongs — had a nearly half billion-year head start on the research and development side of things. To support its tubular body, Euplectella aspergillum employs two sets of parallel diagonal skeletal struts, which intersect over and are fused to an underlying square grid, to form a robust checkerboard-like pattern.

The discovery of symmetric geometric patterns in living organisms is not new. Ernst Haeckel’s marvelous book Art Forms in Nature analyzes the geometric structure of tiny creatures called Radiolaria. The variety of geometric patterns created by nature and beautifully illustrated in his 1862 book is breathtaking. What is startling about the geometry of marine sponges, however, is that the orthogonality of their skeletal structures is something that one might expect to find in plants or animals on the surface of the earth where gravity translates structurally into perpendicularity. But in the amorphous sea, orthogonality is a puzzling occurrence. And if that right-angle geometry is not enough on its own, the overlaid 45-degree rotation of the orthogonal grid to enhance the structural performance is mind-boggling. How did evolution ever create this rotation. One must never underestimate the creative powers of Chance and Necessity.

F-117 NighthawkUS Airforcec.1982

F-117 Nighthawk
US Airforce

Did the Phenomenon of Diagonality create in effect a 20th century zeitgeist, a subconscious state of affairs that allowed for the development of the Lockheed F-117 Nighthawk ground-attack fighter, a plane that used stealth technology to make it nearly invisible to radar? It was designed to have a tiny radar cross section. Contrary to the trend of most planes to be smoothly aerodynamic in profile, the stealth is angular with sharp edges and flat planes.

For certain, the design of this plane was not the result of an aeronautical engineer wanting to design an aircraft expressive of the 20th century’s dominant geometric design motif. However, the question remains as to whether the pervasive use of diagonals in all fields of design since the beginning of the 20th century established a fertile ground of creativity and an unconventional geometry so that angular designs in aircraft could even be considered. Did the Phenomenon of Diagonality create in effect a subconcious license to entertain angularity where aerodynamic curves before then had been the ruling geometry?

A 1964 paper published by a Soviet mathematician titled “Method Edge Waves in the Physical Theory of Diffraction” triggered this innovative approach to stealth technology. However, was it the daring use of diagonals in other fields that paved the way for the next step; the design of a faceted airship in which diagonals occur on every surface plane of the aircraft and even in the jagged profile of the windshield frames? Was there something more than coincidence between the Soviet mathematician’s paper and the flare of designs in many fields using the diagonal motif in the early 1960s? One is inclined to wonder whether there is a more direct (but not intentional) cause-and-effect relationship and not just a coincidence that resulted in the angular design of the F-117 Nighthawk Stealth Bomber.

Max Reinhardt Haus, projectPeter Eisenman, architect1982

Max Reinhardt Haus, project
Peter Eisenman, architect

The Max Reinhardt Haus project was designed for a site in Berlin by American architect Peter Eisenman. Inspired by the geometry of the Mobius strip, the 420 foot building rises in one location and, after twisting and arching through space, comes down on a plot immediately adjacent thereto with its axis shifted and displaced. What starts out as a glass wall, becomes a glass roof and a glass floor in a form that is as much sculpture as it is architecture.

Directly across the Spree River is a triangular site in front of the main railroad station for which Ludwig Mies van der Rohe designed his influential project for the first glass skyscraper in 1921. A then daring proposal for office building floors that taper to sharp wedge-shaped forms similar to the main skylighted space at the East Wing of the National Gallery in Washington, D.C.

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