You have a square thin piece of paper, 1-inch side. Can you, using only a blade (or a pair of scissors or whatever), make a hole in this paper and through it pass a solid sphere with diameter, say, 5 inches?

+--------+
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|        |
|        |
| ------ |
|        |
|        |
|        |
+--------+

The above is the square with a slit across the midline to within .01 inch of the sides.

The largest sphere would have circumference .98 inch. Diameter=.3119

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| -----+ |
+----- | |
| -----+ |
|        |
|        |
|        |
+--------+

These new cuts also leave a distance of .01 inch from the sides and other cuts.  The new hole has an effetive circumference of approximately .98*2 + .97*2 + .02 = 3.92

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|        |
| -----+ |
+----- | |
| -----+ |
+----- | |
| -----+ |
|        |
+--------+

Each set of new cuts extends the diameter by .98+.97+.02 = 1.97 inches.

The circumference of the ball is about 15.8 inches. 

Theoreticaly you could get by with only 7 squiggles like this, but there is room for 49 of them.  If you were careful enough (or had a fine computer controled laser cutter and strong paper) you could probably fit this around a basketball.

 

Posted by Jer on 2005-10-03 14:10:14