By James Wolf – September 2026

One of the most visually surprising forms in bamboo architecture is the hyperbolic paraboloid—a doubly curved surface that can be constructed almost entirely from straight structural members.

This is an anticlastic surface: its two principal curves move in opposite directions. More importantly for builders, the hyperbolic paraboloid is also a doubly ruled surface. Two families of straight lines can pass through every point on the surface.

In practical terms, this means that straight pieces of bamboo can be arranged to produce something that appears fluid, curved and highly complex.

That combination—simple components creating sophisticated geometry—is one of the reasons the hyperbolic paraboloid, often shortened to hypar, is so well suited to bamboo construction.

From Mathematics to Architecture

The hyperbolic paraboloid was understood mathematically long before it became a recognizable architectural form. Its development in construction belongs to a broader history of engineers and architects experimenting with ruled surfaces, shell structures and double curvature.

Russian engineer Vladimir Shukhov was among the earliest pioneers of doubly ruled structures. Beginning in the late nineteenth century, he demonstrated that grids of straight steel members could create strong, lightweight hyperboloid towers. His famous water tower for the 1896 All-Russia Exhibition is an important milestone in the history of ruled structural surfaces.

A hyperboloid and a hyperbolic paraboloid are different geometries, so Shukhov should not be described as the inventor of the hypar roof. Nevertheless, his work established an important structural idea: a form that appears continuously curved can be generated from repeated straight elements.

Catalan architect Antoni Gaudí later explored true hyperbolic paraboloid geometries in his architectural work, particularly at the Colònia Güell church and the Sagrada Família. Gaudí understood that ruled geometry could unite structure, construction and architectural expression.

During the 1930s, French engineers Fernand Aimond and Bernard Laffaille helped turn the hyperbolic paraboloid into a practical structural system. Their analytical and experimental work contributed to the development of thin concrete shells that could cover substantial areas with very little material.

Félix Candela and the Golden Age of the Hypar

The architect-engineer most closely associated with hyperbolic paraboloid construction is Félix Candela.

Working primarily in Mexico during the 1950s and early 1960s, Candela used reinforced concrete to create exceptionally thin shell roofs. His designs demonstrated that dramatic architectural curves did not necessarily require complicated curved formwork. Because a hypar can be generated from straight lines, the formwork could be assembled using ordinary straight timber boards.

Candela described the hyperbolic paraboloid as one of the easiest and most practical shell forms to construct. Projects such as the Cosmic Rays Pavilion at the National Autonomous University of Mexico and Los Manantiales restaurant at Xochimilco transformed an abstract mathematical surface into expressive, efficient architecture.

Engineers and architects including Eduardo Torroja, Eduardo Catalano, Le Corbusier, Iannis Xenakis and others also explored related shell and ruled-surface geometries. By the 1950s and 1960s, hypar roofs appeared in churches, factories, exhibition buildings, airport terminals, gas stations and roadside structures around the world.

The basic lesson was compelling: curvature creates stiffness, while ruled geometry keeps construction relatively straightforward.

Why the Hyperbolic Paraboloid Works So Well with Bamboo

Bamboo is naturally linear. A well-selected bamboo pole is strong, light and relatively straight, but designers often want bamboo architecture to feel organic and curvilinear.

The hyperbolic paraboloid provides a bridge between these two conditions.

Rather than forcing large bamboo poles into difficult curves, builders can arrange straight poles along the surface’s two ruling directions. From a distance, the combined lattice reads as one continuous, sweeping form. The structure can create a roof, a wall, an entrance or all three simultaneously.

The crossing grid also helps distribute loads through the surface instead of relying only on conventional beams and columns. Depending on the span, geometry, connections and structural design, the system can combine arching action, tension, compression and overall shell stiffness.

This does not mean that every bamboo lattice shaped like a saddle automatically becomes an efficient structural shell. The boundary members, foundations, connections, pole selection and resistance to wind and asymmetric loading must all be considered. For permanent buildings, the system should be developed and verified with a qualified structural engineer familiar with bamboo.

When properly designed, however, the hypar offers several important advantages:

• Complex-looking curved architecture made from straight poles
• Efficient use of a naturally linear material
• Large, open and shaded spaces
• Repetition of relatively simple components
• Strong architectural identity with minimal material
• The ability to combine roof, wall and structural expression

An Early Bamboo Exploration in Southeast Asia

These photos document Bamboo Village, built in Vietnam in 1997. I worked on the project as bamboo construction consultant and project manager.

The entrance structures and principal gathering space used opposing families of straight bamboo poles to generate saddle-like, double-curved forms. Although the individual members were straight, their changing angles created the visual impression of continuous curvature.

The technique was especially effective at the entrances. The bamboo grids rose from the sides, twisted across the span and descended again, creating gateways that felt simultaneously natural, structural and ceremonial.

Inside the larger pavilion, the intersecting bamboo members helped define an expansive tropical space beneath the thatched roof. The structure remained visually light and permeable, allowing air, views and filtered daylight to pass through it.

This project was completed years before hyperbolic paraboloid construction became widely discussed through today’s bamboo schools, workshops and social media. I do not present it as proof of the world’s first bamboo hypar. Bamboo building traditions have developed across many regions, and early work is often poorly documented. It is, however, a clear example of designers and craftspeople exploring ruled, double-curved bamboo geometry at an earlier stage in the contemporary bamboo movement.

Jörg Stamm and the Popularization of Bamboo Hypars

Any contemporary discussion of structural bamboo should acknowledge Jörg Stamm—also frequently written online as Jorg Stamm—the German carpenter and bamboo builder whose work has connected European carpentry knowledge with the bamboo traditions of Colombia and Southeast Asia.

Stamm began working with bamboo in Colombia during the 1990s. His bridges, public structures, workshops and later projects in Indonesia helped disseminate a practical, structurally ambitious approach to bamboo construction. His contribution goes far beyond one particular form: he helped demonstrate that bamboo could be treated as a serious engineering and construction material.

His work in Bali, including his involvement with John Hardy, Green School Bali and the wider community that later grew around Bamboo U and IBUKU, brought these ideas to a much larger international audience. The collaborations between Jorg Stamm, Ibuku and James Wolf lead to the 2021 Architectural Masterprize winning structure, The Arc at the Green School in Bali.

Another example is the Bamboo Hall at the Bamboo U campus in Bali. Designed by Jörg Stamm and Jules de Laage and partly constructed during a Bamboo U course in August 2019, the building combines seven interlocking hyperbolic paraboloids supported on nine foundation points. The surfaces flow between roof and wall, creating a large multifunctional space integrated into the sloping site.

Through projects such as this—and through teaching, workshops and publications—Stamm and the Bamboo U community have helped popularize the hyperbolic paraboloid as part of the contemporary vocabulary of bamboo architecture.

Recognizing that contribution does not mean that the method suddenly began in Bali. It belongs to a much longer evolution: from mathematical geometry and Shukhov’s ruled structures, through Gaudí’s experiments and Candela’s concrete shells, to early bamboo applications in Latin America and Asia.

A Geometry Made for Bamboo

The hyperbolic paraboloid reveals something fundamental about bamboo design: organic architecture does not always require bending the material into organic shapes.

Sometimes the most expressive curves emerge from an intelligent arrangement of straight elements.

This is where geometry becomes a tool of craft. A builder can work with the natural characteristics of bamboo rather than against them. Repetition creates curvature. Curvature creates stiffness. Structure becomes ornament, and ornament becomes structure.

Today, digital modeling and parametric design make hypar forms easier to visualize and modify. But the underlying principle remains wonderfully direct. With four boundary points, two families of straight members and a clear understanding of structural behavior, a simple bamboo pole can become part of a remarkably sophisticated architectural surface.

For me, that is one of the enduring attractions of bamboo architecture: achieving more not by imposing complexity on the material, but by discovering the complexity already available through geometry.