It's Christmas and you've been given the latest 3D puzzle. You've looked at it for ages and from all sorts of angles, but you still can't solve it.
But then you meet someone who has a different perspective. Suddenly the answer is clear.
A different formula
Scientists have all sorts of puzzles to solve. Many are extremely complex.
The movement of objects through space is an example. There are all sorts of forces at work, such as the gravitational pulls of nearby stars and planets.
Conventional algebra - the version you learn in school - works in simple situations. It explains why apples fall to the ground and how fast they fall. But it struggles to cope with complex three-dimensional problems. Even the most powerful computers can't do the sums fast enough.
So is there a different formula you can apply? Supported by PPARC, scientists at the University of Cambridge found there is.
In the nineteenth century, Cambridge mathematician W.K. Clifford invented a different type of algebra - one that made three-dimensional problems easier to solve.
Called geometric algebra, scientists now use it in all sorts of situations. To describe how particles move in atoms and how objects move in space, for example.
A profitable solution
Recently the University's scientists have applied their world-leading expertise to a completely different type of space - cyberspace.
Computer games have advanced a lot since Pac-Man. Many are set in virtual worlds - past, present and future.
The graphics are 'awesome' but not quite perfect. It takes too long for computers to work out exactly how light and shade should fall on objects as they move.
The Cambridge scientists found their way of doing the calculations was much faster. Ten to 100 times faster - enough to allow manufacturers to make their games much more realistic. Truly awesome, in fact.
To exploit the opportunity, the scientists set up Geomerics in 2005. The company is backed by venture capitalists and a PPARC Enterprise Fellowship.
Geomerics produces software for use by games designers, film makers and others. They all need virtual reality worlds that are realistically lit.
Already the software has attracted big interest.
Globally more than US$20 billion is spent on computer games each year. It's a competitive market so manufacturers are constantly trying to outdo each other, especially in the quality of their computer graphics.
In their quest, they spend more than US$600 million a year on software and other technologies.
Geomerics plans to win a share of this lucrative market.
The computer and video games industry is one of Britain's big success stories.
According to ScreenDigest, it earned Britain close to £200 million in 2003. Exports were worth almost £500 million that year, but only £290 million was spent on imports.
Some 22,000 people are employed in the industry. Just over 6,000 of them work for games development companies.
Geomerics' technology will also benefit other industries.
It makes it easier for mobile phone companies to design their antennas, for example. And it will help the defence industry reduce the radar signatures of ships and planes, protecting them against attack.
Source: PPARC
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