O'Really?

June 12, 2006

Bend it like Bezier?

Football informatics, theory and practice: Germany 2006

Bayern BallThe frenchman Pierre Bézier knew a thing or two about curves. But as World Cup fever tightens its grip around the globe, it is the footballers in Germany who are showing us just how much they know about the practical science of curving and bending the ball into the goal. Is there any essential curve-theory for World Cup stars like Beckham, Ronaldinho and Thierry Henry to read and brush-up on in their German hotels this summer?

Sports scientist Dr Ken Bray from the University of Bath in the UK hopes that sportsmen and spectators alike will be reading his new book How to Score – Science and the Beautiful Game. This is another popular science book that tries to make fluid dynamics accessible to the layman. In publicising his new book, Ken points out that the new Adidas Teamgeist™ football will unsettle goalkeepers at the World Cup, because the balls move more in the air than traditional ones. This smells of marketing-hype, both for the ball and the book, but it is interesting and topical nonetheless.

Mathematicians and numerical analysts have known for years, the really essential reading for footballers this summer is the famous curves index. These wonderful web pages, free online and completely devoid of hype, describe all the equations for putting the ball in the back of the net in great style. After reading these pages, perhaps World Cup footballers will be able to curve the unpredictable Teamgeist™ ball even more lavishly than before. Just imagine the confusion of a goalkeeper facing a free-kick, when the ball follows a right strophoid curve: y2 = x2(a – x)/(a + x)! This would certainly be more entertaining than the all too predictable and common straight line: y = mx + c that soars over the bar and into row Z of the spectators behind the goal…

Whether scientists, footballers or spectators, we can all enjoy the science of curving at the World Cup in Germany this summer. Bis Bald Berlin!

References

  1. Bend it Like Beckham: The curve ball free-kick (France 1998)
  2. Bénd it Like Bézier: The Bézier Curve
  3. Bend it like Brazil: A perfect example of a free-kick by Roberto Carlos
  4. Bend it like Euclid: Is a straight line a curve?
  5. Computer Graphics: Curves and Surfaces, Bézier representations
  6. From the beautiful game to the computiful game: Nature catches football fever
  7. Goal fever at the World Cup: Why the first strike counts
  8. This post was originally published on nodalpoint with comments

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