Every curved shell of the Sydney Opera House roof is a section cut from the same imaginary sphere.

When Danish architect Jørn Utzon won the 1957 design competition for the Sydney Opera House, his sail-like sketches were so structurally complex that engineers spent years unable to figure out how to actually build the roof’s curved shells. Every proposed shape produced different geometry that would have required custom formwork and calculations for nearly every section, making construction prohibitively expensive.

The breakthrough came when Utzon realized that if every shell was cut from the surface of one single, enormous imaginary sphere, all the individual roof panels could be built from the same standardized, repeatable pieces of precast concrete rib. Utzon later described arriving at the idea while peeling an orange, noticing how any segment cut from it shared the same curvature as the whole fruit. That single insight turned an unbuildable design into one of the most recognizable buildings in the world, though the project still took 14 years and ran vastly over budget before opening in 1973.