## Mathematician has formula for success at Olympics

The Canadian rowers who won gold in the men's eight race in the 2008 Olympics in Beijing owe their success, at least in part, to Karl Adam, the innovative German coach whose teams dominated the sport in the 1950s and 1960s.

Adam invented the German rig (also known as the bucket or Ratzeburg rig), which departed from the usual, alternating left-right rowers' position. He placed his boys left-right-right-left-right-left-left-right. Their positioning was designed to prevent the reed-thin, 20-metre sculls from wiggling as the sweeping oar strokes exerted pressure on, then away, from the hull. A boat that wiggles creates more water resistance than one that doesn't, and is therefore slower, perhaps 1 per cent slower, according to some estimates.

John D. Barrow, a renowned mathematician, cosmologist, author and all-round sports nut from Cambridge University, turned the wiggle-free rowers' placement into a mathematical equation. It is incomprehensible to normal humans and probably some math-challenged coaches. But none of the modern coaches dares to use the old-style rowing pattern.

Not only did Barrow figure out the equation, he used it to invent two other positioning patterns for the men's eight, which may or may not be used at the Olympics in London this summer. The story of his work on rowing math forms a chapter in his entertaining new book, 100 Essential Things You Didn't Know You Didn't Know About Sport (published by The Bodley Head).

Barrow is 59 and looks like an athlete. In his youth, when he attended Ealing Grammar School in London, he was a middle distance runner. He remains active and is the father of sports-mad children – his daughter is a professional ice-skating coach. He is now director of the Millennium Mathematics Project at Cambridge and Gresham professor of geometry at Gresham College in London.

His résumé makes the average overachiever look like a slug: 22 books published, including The Infinite Book: A Short Guides to the Boundless, Timeless and Endless, 32 major awards, author of hundreds of research papers. When he is not thinking about spirituality and the universe, he is thinking about sports – that is, how math can explain sports and improve athletes' performance. "I owe many, many things to sports," he says in the courtyard of Gresham College.

Barrow says he used sports as a technique to make math more enjoyable to students. "If you link the two together – sport and math – you get the kids interested," he says.

The teaching technique, combined with his love for all things athletic, resulted in the book. You name it, it's in there.

Want to know why the air over the track in a velodrome is heated. It's because warm air is slightly less dense that cool air, allowing the track bikers to zip around the oval at slightly higher speeds. Barrow estimates it makes the bikers 1.5 seconds faster in the four-kilometre team pursuit event.

Ever wonder why swimming records get broken all the time but running records can last for a decade or so? A fascinating chapter called "Total Immersion" reveals that swimming, the most technical sport, is the sport which that has benefited the most from mathematical research. Coaches, using fluid dynamics (the science of water in motion) have turned swimmers into human torpedoes by minimizing the drag effects of water pressure, friction and waves on the swimmers' bodies.

This is done by such things as finely tuning the angle at which the swimmers' hands cut the water and staying underwater longer after their turns, all the better to eliminate the drag of surface waves.

The result has been a dramatic increase in the times of swimmers. In 1964, the world record for the 100-metre men's freestyle was 52.9 seconds. Today, it's 46.9 seconds, an 11.3-per-cent improvement. Compare this to running. In the 400-metre event (a race that takes roughly as long as the 100-metre swimming race), the 1964 record was 44.9 seconds for men. Today it's 43.18 seconds, an improvement of just 3.8 per cent.

Barrow uses math not only to explain athletic improvements, but also to point out the fundamental unfairness of some events. The triathlon, which combines swimming, biking and running, in that order, is a "strange event because, if you look at it with the mathematical eye, there is a ridiculous bias toward biking."

The time required to do the centre stage – 40 kilometres of biking – vastly outweighs the time required to do the relatively short swimming and running stages on either side. The result is that the best bikers, not necessarily the best triathlon athletes, have the greatest chance of winning. Barrow calls this sport "a writeoff, one in great need of revision."

Barrow thinks math can explain just about everything, which is why he's already contemplating a book on math and art. He notes, for instance, that you can use math to detect art forgeries, because equations exist that govern paint-cracking patterns.

His publisher is probably wondering whether he's done the math on the potential profit stream from number-literate books.