Hyperbolic Paraboloid Surface
Since the mid-20th century, one of the interesting and popular mathematical forms for architects. It is the Quadric Surface equation of the Hyperbolic Paraboloid. According to Erik Demaine;
“Hypars and joining hypars in a few special ways have been used extensively in architecture. For example, Curt Siegel’s 1962 book Structure and Form in Modern Architecture illustrates the roof of the Girls’ Grammar School in London (designed by Chamberlin, Powell, and Bonn) which is what we call a “5-hat” with five hypars spread apart slightly.
Later, the idea of joining two 5-hats is suggested, although the two hats are cut to have a curved boundary, making them easy to join. Page 260 shows a photo of the Philips pavilion at the 1958 Brussels exhibition (designed by Le Corbusier) which is a beautiful surface made of eight or so hypars that rests on the ground. Heinrich Engel illustrates a few more wonderful examples with straight boundaries in his book, each involving between five and twelve hypars. Finally, Frei Otto illustrated and analyzed a grid of connecting “4-hats” in the 1969 book Tensile Structures.”
It was a great pleasure for me to model this ancient math shape. I saw its neverending potential as also freshly valid for today’s digital design paradigm. Here is the Grasshopper definition of the Hyperbolic Paraboloid Surface you can download:
I added a planar rotation in the parametric model so that it turns without changing the overall shape. At some point (actually at degree “pi”) it creates the other famous z=xy surface known in architecture. We should also deal with that.