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Published on July 3rd, 2014 | by Liam

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Having a ball at the World Cup

Soccer, or football, is the most popular sport in the world, and the World Cup is its biggest tournament. Maths+StatsRight now, millions of people are cheering for their teams, hoping for victory. But before the first match kicked off, scientists and mathematicians joined forces to answer a very difficult question – how do we design the perfect soccer ball?

The perfect soccer ball would be a sphere. But soccer balls are usually made from rubber or leather, and these materials come in flat sheets. To turn these flat sheets into round balls, designers cut many smaller shapes called panels, and sew them together.

There’s no perfect way to make a sphere out of flat panels, but there are plenty of mathematical shapes that would make a good starting point. You could start with the Platonic solids – solid shapes where every angle, face and side are the same. There are five Platonic solids, ranging from the triangular pyramid and the cube, all the way up to the twenty-faced icosahedron.

There were two different balls used during the 1930 World Cup. One design was made of six H-shaped panels. These were sewn together in a cubic arrangement: top, bottom, left, right, front and back. The other design had more panels – six squarish faces were each made of two or more strips, in a design that is still used for volleyballs. For 40 years, the World Cup used different designs for its balls. But each design had the same cubic structure: top, bottom, left, right, front and back.

For the 1970 World Cup, Adidas supplied a ball with a brand new design. It was based on the twenty-faced Platonic icosahedron. To make the ball rounder, they used an icosahedron with its corners cut off – a truncated icosahedron, otherwise known as a buckyball. This ball, made from 20 white hexagons and 12 black pentagons, became the standard shape for soccer balls.

In the past 40 years, the materials and techniques used to make soccer balls have improved. The panels used to make soccer balls are moulded round, not flat, so new designs don’t need as many pieces. In 2010, the Jabulani ball had eight panels. This year’s Brazuca design has only six panels, arranged in a cubic structure. Cubic design, seen in the first World Cup balls, is back again!

More information
Interactive history of World Cup balls
Every World Cup goal 1930–2010
Designers fine-tune ball aerodynamics (very advanced and pdf)

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