## Chapter 11: The Spherical Solution (Part 2)

Various myths surround the discovery of the spherical solution. Dominant among them is the idea that Utzon derived it from an orange. Whilst it is true that the solution can be demonstrated by peeling an orange in a certain way, it had in fact been Eero Saarinen who, over breakfast one morning years earlier cut into a grapefruit to derive the shapes of the TWA Building. He later used an orange to explain the shape of the shells.

Utzon had returned from his meeting with Zunz and Arup excited by the ribbed expression of the soffit of the shells. However, significant problems remained unresolved, including the requirement that each rib still be unique, because of adherence to the existing paraboloid geometry.

Zunz and his number two, John Lethebridge, discussed with Utzon the 'geometric straitjacket' that a non-repetitive form yielded, and explained that repetitive structure could only be extracted from spherical or toroidal forms. In fact, it can also be derived from ellipsoid geometry.

Arup's consistent advice to Utzon over the years that he should look for a repetitive geometry – now soundly reinforced by Zunz and Lethebridge – must have left Utzon with little doubt that they were right: it was now a question of how it might be achieved.

The solution of tiles to cover the finished shells also called for a repetitive geometry. Since 1958, Utzon had been concerned with the solution, even suggesting to Mikami that they could perhaps pursue the round tiles Saarinen had used on the TWA Building. This would leave the pattern to the tilers and the architects would not have to produce drawings. The irreverence of even contemplating this approach suggested that Utzon was genuinely struggling with the answer at the time. The outstanding beauty of the final solution for the tiles is another indication of the brilliance of the spherical solution to the roof.

By his own account, Utzon was alone at the Helleb�k office one evening, with these considerations very much weighing on his mind. While stacking the shells of the large model to make space, he was surprised to notice how similar the shapes appeared to be in this context. Previously, each shell had seemed distinct from the other, but now it struck him that if they were so similar, perhaps each could be derived from a single constant form, such as the plane of a sphere.

The simplicity of the idea appealed very much to Utzon. It would mean that not only the building's form could be prefabricated from a repetitive geometry, but that a uniform pattern could also be achieved for the tiling of the exterior surface. It was the binding discovery that allowed for the distinctive characteristics of Sydney Opera House to be finally realised. The vaulted arches, the exceptionally beautiful finish of the tiles and the timeless sail-like silhouette of the house all derive from his decision to move the form to a spherical geometry.

It also shifted the principle of the design away from the expression of a style, in this case shell architecture, to the more permanent idea inherent in the universal geometry of the sphere.

Whilst it is clear that many considerations contributed to the decision, for Utzon, the realisation was profound. His assistants were stunned when he explained the idea and set to providing drawings that would prove its validity.

By finding the part of a sphere that best suited the existing shapes of the shells, each new form could be extracted. Furthermore, one profile was all that was required as this would be mirrored to complete the arch. The minor hall of Sydney Opera House is identical to the major hall except in scale.

Once the theory was confirmed through drafts, Utzon phoned Arup in London, shouting excitedly down the phone that he had solved the problem. Unable to seize the concept over the phone and without the aid of instantaneous imaging, or even a fax machine, Arup promised to come quickly.

Meantime, Utzon had the Helsingør Shipyards create a wooden model of the top of a sphere, with meridian lines emanating from the pole at a constant angle of 3.65 degrees. These showed the ribs, each identical to the other and therefore ideal for prefabrication. Each shell was clearly demarked and emanated from the zenith point of the spherical model.

By any standard it was a beautiful solution to these crucial problems, which elevated the architecture beyond mere style and timelessly expressed the fusion between design and engineering.