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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: Soccer Ball
Replies: 6   Last Post: Jun 3, 1994 11:09 AM

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John Sullivan

Posts: 14
Registered: 12/6/04
Re: Soccer ball
Posted: Jun 2, 1994 3:43 PM
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[forwarded]

This question from Mark Saul <73047.3156@CompuServe.COM>
came to me via Dick Askey and Dennis Stanton:
> Speaking of mathematicians' help, can anyone tell me WHY the
> soccer ball is constructed as it is? Why, for example, is it not
> made of spherical triangles, sewn together to make an icosahedron?
> Is the soccer ball the answer to some well-known minimal problem?:
> Does it minimize stitching? or deviation from a sphere? or stresss
> when stuffed? Or is it just pretty?


I'm not sure if there's any nice problem for which the soccer ball
is minimal. One nice unsolved problem for polyhedra is to minimize
the total edge length, with fixed enclosed volume. But it seems the
solution to this one is probably a triangular pyramid. This probably
corresponds to the minimal stitching question.

As a wild guess about soccer balls, I'd point out that this is the
largest polyhedron with three-fold vertices. Perhaps it is harder
to get something to stay together when there are more than three
faces meeting at one point. So with this restriction, the soccer
ball is the closest you can get to a sphere among the Archimedean
solids.

Maybe someone else will have further ideas. Of course, it _is_ pretty.

-John Sullivan






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