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Topic: Accessible problems
Replies: 5   Last Post: Apr 27, 1995 9:09 PM

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Rex Boggs

Posts: 12
Registered: 12/6/04
Re: Accessible problems
Posted: Apr 27, 1995 3:29 AM
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Ian Stewart, in his excellent book Game Set and Math, had a nice little
story about Mother Worm's Blanket.

Esentially, Junior Worm is a squiggly little thing exactly one unit long.
His mum wants to cover him with a blanket while he sleeps (while he is
sleeping he is not moving). Father Worm, being frugul, wants to make the
blanket as small as possible and still be able to position it so Junior is
completely covered by the blanket when he is sleeping.

The question is, 'What is the smallest blanket that meets this criterion?'
Certainly a circular blanket of radius 1 will work, since no point on Junior
is more than 1 unit from the tip of his tail. But can you make it smaller?

Indeed you can! But no one knows what the minimal area is. This is a nice
little problem because the more you work on it, the more you can see ways to
reduce the area. The article gets the blanket down to a semi-circle of
radius .5, and implies that the best solution to date was an area of pi/8.

Cheers

Rex






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