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 Figure Eights (Posted on 2005-02-15)
Suppose that I drew an infinite number of disjoint closed curves in the plane (such as circles, squares, etc.). Suppose that I then tell you that there is one curve for each positive real number.

You would not have too much trouble believing my assertions at this point. For example, I could have drawn all circles with center at the origin. They are all disjoint, and for each positive real number x, there is a corresponding circle - namely, the circle of radius x.

But suppose that I also tell you that all the curves I drew were figure eights. Can you believe my assertions now?

(A figure eight is a curve in the plane obtained from the basic "8" shape by any combination of translation, rotation, expansion, or shrinking.)

 See The Solution Submitted by David Shin Rating: 4.2000 (5 votes)

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 re: This may work! | Comment 15 of 34 |
(In reply to This may work! by np_rt)

Indeed those are not disjoint, since they share a crossing point.
 Posted by Charlie on 2005-02-16 13:27:11

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