From: mathwft@math.canterbury.ac.nz (Bill Taylor)
Newsgroups: sci.math
Subject: Pseudo-paradox recalling BANACH-TARSKI.
Date: 6 Sep 1997 02:39:46 GMT

This lovely thing is too hard to reproduce in ascii, so I urge you all to
have a look at the article it came in...

Mathematical Intelligencer; vol 19,  #3,  page 66.

It is a lovely article, with illustrations, showing a partition of the
hyperbolic plane, H, such that

H = A u B u C;
A, B, C are all congruent; but
A is congruent to  B u C.

Very neat!  As the authors observe, it is reminiscent of the B-T paradox,
but altogether quite different, in that the sets are measurable, specific,
and in fact fairly straightforward.

It's a beauty!

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             Bill Taylor            W.Taylor@math.canterbury.ac.nz
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     Any sufficiently primitive magic is indistinguishable from science.
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