Sydney Opera House

The curvature geometry of the shells as build are a regular sphere.

The original design was a free hand shape by Utzon himself.

According to Mikami, Utzon defined the cross section geometry with 4mm square acrylic stick stood right on a table and the top end shifted horizontally. This is special case of Elastica curve. Arup engineer approximated the Elastica curve with Parabola. The Parabola was also used to define longitudinal section. [1112/SK2B,1958, page 41, Mikami] In 1961 Utzon came to find solution to standardize the construction of the shell by making all shells cut from a sphere. However in the film footage Utzon uses a model with Parabolic or Ellipsoid solid, not part of sphere. Story told today seem to over-simplify the fact that he used Ellipsoid or Parabolic Sphere first, then made further refinement with Regular Sphere.

"The Edge of the Possible", 17:32