Maths of the Sydney Opera House: Nature Inspiring Design


Copyright © Sydney Opera House Trust.

About this video

What is fractal geometry and how did it help build the Opera House? Learn about how architect Jørn Utzon took inspiration from the natural environment to reflect its the harbourside location of the building with Eddie Woo and Richard Johnson, an architect who worked directly with Utzon. 

Maths of the Sydney Opera House is a four part video series with award-winning maths teacher, author and Wootube star Eddie Woo uncovering the mathematical concepts behind the construction and design solutions of Opera House.

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- Port Jackson, the Harbor Bridge, and the Opera House have been called, "The Visual Trinity of Sydney." The brilliant white of the Opera House is like a pearl in the midst of Port Jackson. While the geometry of the shells evokes the sails of a mighty galleon as it extends from Bennelong Point out into the harbor. What aspects of his design and architectural language explain the deep way that it speaks to the souls of people from all around the world? And what does any of that have to do with mathematics? Every part of the world has its own unique architectural style. Buildings in Europe are different to buildings in Asia, which are different again to those in Africa and the islands of the Pacific, but more than 10 million people from all around the world, more than double the population of Sydney itself, visit the Sydney Opera House every single year because Jorn Utzon gave the building universal qualities that appeal to people from all cultures. That universality comes from something that every human being experiences, no matter where they come from, the geometry of nature. Let's take a walk around the building with someone who knows that geometry and also knew Utzon. Richard, the Sydney Opera House, it truly is a monument to human ingenuity and the built environment. But can you tell me what it means that Utzon was inspired by nature in how he chose his geometry?

- Well, he was always an extraordinary passionate of nature and what he could learn from it. And he was interested in the growth patterns of plants. And it's such a rare capacity to fuse strict geometry and achieve the freedom of form, in a sense, like you see in nature.

- Well, I think we often... If we said to someone to use rigid geometry, we might imagine them coming up with something very fixed straight lines, which is almost the exact opposite of what we have here.

- Absolutely, but the same rigor, geometric rigor, is here as is in a building with straight lines and right angles, and that's the brilliance of it.

- Utzon's design evokes several natural forms of geometry. For instance, the leaning shells remind passersby of the crashing waves on a beach, a perfect image given their maritime setting. Utzon was also inspired by tree leaves. The cut of each shell does look like an individual leaf that's come to rest on the ground, but leaves themselves have some amazing mathematics within them that the Opera House alludes to. All tree leaves have a fine vein structure that allows them to deliver water for photosynthesis. Those veins are arranged in a pattern called a fractal, which takes the same shape copied over and over again except at smaller and smaller scales. Not only do the shells look like leaves, but they're covered with tiles like fractals. Each shell is made of ribs, each rib is made of chevrons, and each chevron is made of individual tiles. This geometry is what makes the Sydney Opera House not just impressive from a distance, but even more beautiful up close. The visual experience as you approach the Sydney Opera House was at the front of Utzon's mind as he designed the building.

- For Utzon, the beginning and the end of every architectural exploration was how people reacted. In this particular building, an important part of the human experience is preparing yourself for the theater. You leave your everyday life. You walk across a piatsa connected to the harbor setting, you mount a hundred meter wide staircase, you come up onto the platform, you're up above the every day. Just like the Mayans came up to the platform to commune with the gods, we are up on this platform, preparing ourselves to enter the auditorium.

- In what way to the geometry and materials of the Opera House respond perfectly to the light of Sydney?

- Utzon was a sailor. His father was a naval architect. He was used to reading naval maps. He was used to observing the sun, the clouds, and the sea. And he was therefore of a mind to understand this location, but he was also aware, because of being an acute observer of nature, that the sun was higher in this part of the world and sharper. Therefore, any form that's covered in white tile suffered the problem that, with sharp sunlight, you would not see the form. You would see a glare of shape, not the cylindrical form. So he looked at expressing the ribs and the structure using glazed tile and a matte tile to reinforce the geometry, the curvilinear geometry, the cylindrical geometry, so that, even in the harshest sunny light midday of Sydney, you would see the form of the building rendered perfectly.

- Utzon brought a sophisticated understanding of geometry and artistic expression to his design, one that was inspired by the mathematical shapes found in nature: fractal geometry, the curve of a leaf, the crashing waves of a harbor, but his lofty thoughts never took him away from remembering that the Sydney Opera House was always to be a medium for human experience. So he designed every aspect of the building with the perspective of an individual in mind. That's why, to this day, it's such a moving experience to approach and enter the Sydney Opera House.

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