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In new series about Five Shapes, mathematician Marcus du Sautoy finds his favourite forms in some highly unlikely places.
Monday to Friday 19 to 23 September 2005 3.45-4.00pm

He visits a spherical building in Paris, hears music inspired by the symmetries of the cube, finds out why pyramids proliferate at the molecular level and why the bagel is not only good to eat, but a great shape for buildings and cracking codes. But could the most shapeless shape of all - the blob - soon dominate our world?

La Grande Arche de la Defense
La Grande Arche, Paris.
An architectural interpretation of a four-dimensional cube.

Programme 1: The Cube

In the first programme, Marcus explores the cube. Why, he wonders, isn't this highly practical form used more? And what does it look like in four dimensions? 

Its perfect symmetry makes it the ideal shape for packing and stacking - no space is wasted and it doesn't matter which way round you put it on the supermarket shelf. But when Sainsburys put tomato soup in cube-shaped cans, consumers didn't like it. 

Apple's cube-shaped computer was quickly replaced by something more ergonomically curvy - the iMac. And cube-shaped televisions are watched only by the designing elite. 

The cube was the building block of modern architecture - admired for its purity and simplicity. But perhaps it's just a little bit too perfect for mainstream taste. 

But there is one cube that consumers do like. In fact, they're so attached to its form, that damaged cubes, not taste are responsible for the majority of Oxo customer complaints.

Listen again Listen again to Programme 1
The Great Step Pyramid
The Great Step Pyramid of Djoser at Saqqara, Egypt

Programme 2: The Pyramid
                         a classic shape 
                        to bury Pharoahs 
                      a  triangular influence 
                   on modern designers who 
                find inspiration in its simplicity
           Though surprisingly rare in buildings,
        on a smaller scale in nature, omnipresent

Listen again Listen again to Programme 2
The Huge, Shiny Sphere of La Geode
La Geode, in the Parc de la Villette, Paris opened in 1986. It is almost unique in being a near perfect architectural sphere.

Programme 3: The Sphere
As the most economical shape for containing matter, the sphere's perfect form has fascinated the minds of men for millennia. From planets to raindrops, nature adores the sphere.

Since Pythagoras and Plato, Arab and European thinkers believed the planets of the solar system to lie on the surface of concentric crystal spheres, each emitting its peculiar harmony, audible as the "music of the spheres". 

Although nature constructs spheres with ease, it's not the case for designers and manufacturers.

Architects have tried since the Pantheon of Rome in the 2nd century AD to use the form, symbolic of unity, democracy and celestial perfection in cathedrals, mosques and temples. And yet as Marcus discovers, that has never been easy.

The Millennium Dome in Greenwich did not turn out to be the section of the perfect sphere that it was designed to be and a startlingly high number of table-tennis balls don't make it past tests for roundness on to the professional table.

Listen again Listen again to Programme 3
The new HQ of GCHQ
GCHQ's new bagel-shaped HQ, near Cheltenham

Programme 4: The Bagel

The bagel, or torus, is not merely a good shape for baking. As marcus discovers - it's also a good shape for office complexes, code-breaking and maybe even universes.

MArcus this week discovers that, as one of the simplest building blocks in the relatively new and highly versatile subject of topology, the bagel is arguably the most important shape in modern mathematics.

Listen again Listen again to Programme 4
The forty stories of the new, environmently
friendly Swiss Re Building in London.

Programme 5: The Blob

In the finale to our series, Marcus examines The Blob. From globular cartoon characters to curvy cars, or natural shapes such as pine cones and gherkins, the blob has always been part of our landscape. But now they are taking over our cities, as architects have adopted the computer technology used in car design and animation.

Marcus talks to architect Zaha Hadid who has done a number of curvy buildings from the Innsbruck Ski Jump to the tram Station in Strasbourg whose car park mimics the swirls of a magnetic field. Plus the Contemporary Arts Centre in Cincinnati which has curves so tempting they have had to put up a sign saying "no skateboarders". Hadid explains how new technology has facilitated the design of these sites, backed up by her childhood liking for maths and trigonometry.

Closer to home, think of or the new Selfridges building in Birmingham or the Swiss Re on the River Thames - nicknamed The Gherkin by locals. Marcus Du Sautoy talks to two of the mathematicians behind the Swiss Re and finds that they smoothed out the edges on computer to create a shape that was both beautiful yet functional.

But if we now have the software to make perfect designs, do we still need mathematicians to work out equations at the drawing board? Without a doubt. Although computer technology is a great facilitator, in the wrong hands it can lead to bland buildings being designed at the push of a button. If we want to keep uniqueness, Marcus Du Sautoy discovers, we need Mathematicians more now than ever.

Listen again Listen again to Programme 5
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