# Soap provides a clean solution for Olympic pool

By Burkard Polster and Marty Ross

The Age, 25 August 2008

Many consider the swimmers Michael Phelps and Stephanie Rice to be the stars of the Beijing Olympics, but we disagree. For us, the star is the swimming stadium itself, the stunning Water Cube. Just like the Olympic stadium in Munich was the star of the Olympic Games in Munich in 1972. Why? Both stadiums are ingeniously modeled on soap bubbles.

Soap bubbles and soap films fascinate mathematicians because they represent Nature’s solutions to many optimizing problems. For example, a spherical soap bubble solves the problem of enclosing a given volume of air with a surface of smallest possible area. And in general, however soap films or soap bubbles form, their surface tension pulls them into shapes of smallest possible area. By stealing the mathematical soul of soap bubbles and then using it for their own cunning ends, mathematicians have solved problems as diverse as the optimal design of airplane wings and of mining layouts.

To construct the futuristic roofs of the Olympic stadiums in Munich, the architects created pole-and-string models of the roof skeleton and then dipped them in soap solution. They then replicated the resulting soap films, creating roofs of smallest area, and of extraordinary strength and beauty.

Beijing’s Water Cube is modeled on an ideal soap bubble foam. Imagine the Universe as a huge bathtub filled with bubble solution. God jumps in, splashing all the water out, and leaving a Universe filled only with soap bubble foam. Being a Heavenly foam, it divides the Universe into cells of equal volume and smallest surface area.

Nobody knows what this Heavenly foam looks like. Lord Kelvin pondered this in 1887, and suggested a honeycomb structure, a 3D version of the familiar hexagonal division of the plane. Then in the 1990s the physicists Robert Phelan and Denis Weaire found a more efficient division. Unlike Lord Kelvin’s honeycomb, which uses one highly symmetric cell, the Weaire-Phelan division of space is made up of the two irregular shapes.

The façade of the Water Cube, designed by Syndey-based engineer Tristam Carfrae, is based upon Phelan and Weaire’s foam. Cutting the foam at an unusual angle results in the very organic looking panels of the Water Cube. And as for the roof of its Munich predecessor, the Water Cube inherits beauty and extraordinary strength from its bubbly origins.

We have decided to frame a picture of the Water cube. And what better way to do this than with a Water Square: a frame carved out of the beautiful honeycomb tiling, the undisputed (but unproved) favorite for the title of Heavenly division of the plane.

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