Soccer 'Sphere' Kicks Off a Circular Argument
Much has been made over the development of a rounder soccer ball for use in this year's World Cup. But Stanford math professor Keith Devlin tells Scott Simon the quest for a perfect sphere remains a geometric improbability.
SCOTT SIMON, Host:
Adidas has been the official ball maker for every World Cup since 1970. You think they'd publicize that? Every four years, the company designs a new football, or soccer ball, as we call it. It is officially approved by FIFA for World Cup competition. Now, the official ball used for this year's World Cup in Germany has a somewhat different design. It consists of a ball made of 14-wing, or butterfly shaped panels, which designers say makes it lighter and more spherical. So how do we explain all those one nil games? Our math guy will, and he's a World Cup fan.
Keith Devlin, who joins us from the Anchor Hotel in Ship Inn in Porlock Weir, Somerset.
My Gosh, Keith. I almost don't have the time to introduce you when you go on one of these jaunts.
(SOUNDBITE OF LAUGHTER)
KEITH DEVLIN: That's right. I like to squeeze in little bits of vacation in between these business trips.
SIMON: Well, first of all, look. Sorry about Becks and the boys. Okay? England did their best. But in the end...
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DEVLIN: Well, I've jumped ship and I'm now supporting Italy.
SIMON: Oh, (unintelligible) is Italy.
DEVLIN: Yeah. No. Like many Brits, I've always regarded Italy as my second home, and I dream of retiring in Tuscany. I probably never will...
SIMON: Probably on what you make with us, it will become a reality very soon. But let me ask you about this new design. Now, they say it's more spherical.
DEVLIN: Yeah. And, you know, they may be right, because if you look at it, the actual seams are all curved, where with all of the more classic footballs, they're essentially geometric shapes. They made of pentagons and hexagons, which geometrically have straight edges. For many years now, FIFA has required that any official ball is within one and half percent of being a perfect sphere.
SIMON: So is there such a thing as spherical ball?
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SIMON: I mean that the human hand can make?
DEVLIN: The idea of a perfect sphere is really a mathematician's idealization. And the challenge in making footballs was always how close can you get? But no matter how much the designers keep trying to come up with new balls, there are certain mathematical restrictions on what they can do.
In fact, there was a theorem by the 18th century Swiss mathematician Leonard Euler, that says if you take - if you're going to stitch a ball together with pieces of any kind, then if you take V to be the number of corners, or V for vertices, in fact, if E is the number of seems, E is actually for edges, and if F is the number of faces, the number of pieces you have together, then V minus E plus F has to equal two. So the ball designer can change the number of corners and change the number of edges, but then the number of faces is determined by Euler's theorem.
Or if they start with the number of faces they want, then there are restrictions on the number of corners, and the number of edges. So no matter even if Adidas designers say they are not mathematical, which I doubt because the new ball has a mathematical aspects to it, as well. Nevertheless...
SIMON: Mm-hmm.
DEVLIN: ...the design of any soccer ball doesn't just have to obey the rules that FIFA imposes; it has to obey the laws of mathematics, in particular, Euler's equation.
SIMON: Ooh. Ooh. Yeah. But...
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SIMON: But the laws of mathematics can't fine you the way FIFA can. Right?
DEVLIN: No. And I'll bet not many soccer fans know that one.
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DEVLIN: Try that one in the bath tonight.
SIMON: Oh, my. You know, you mathematicians can take the fun out of almost anything. Can't you?
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DEVLIN: I was trying to put the fun into it, Scott.
SIMON: All right, for you.
DEVLIN: I've got to say I've find the new ball much less pleasing than - it's sort of a little bit more curvaceous.
SIMON: Yeah.
DEVLIN: But I like the geometric pleasure of the other one. And, in fact, the classic ball is a shape that occurs in nature. And I don't know anything that occurs in nature that resembles the new football, I'm afraid.
SIMON: So let me get this straight. A sphere is theoretical. There's no such thing as a - I mean, it's something that you mathematicians can conceive of, but it's something that we cannot execute.
DEVLIN: That's not really the case. The Gravity Probe B, the gravitational detector that was launched a couple of years ago, that was had to be one of the most perfectly made spheres ever. And that was within a very, very small fraction of being a perfect sphere. And I believe that is the most perfect sphere that humans have ever constructed.
SIMON: Hmm. Well, you wouldn't kick that, would you?
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DEVLIN: You wouldn't want to kick that. No. And it was - first of all, it's made out of metal. And it's also worth an awful lot of money because it took a huge amount of design...
SIMON: Yeah.
DEVLIN: ...to create something with that degree of sphericity.
SIMON: Well, that degree of sphericity. I love that phrase.
(SOUNDBITE OF LAUGHTER)
DEVLIN: Mathematicians can bend a phrase as easily as Beckham can bend the ball.
SIMON: Thank you, Keith.
(SOUNDBITE OF LAUGHTER)
SIMON: Keith Devlin is our math guy, executive director of the Center for the Study of Language, Information and Football, at Stanford University. His most recent book is The Math Instinct: Why You're a Mathematical Genius Along with Lobsters, Birds, Cats and Dogs.
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