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From: A.J.Cribbin@bradford.ac.uk (a.j.cribbin)
Subject: Line: sausage machine
Date: 1995/04/27
Message-ID: <3nohu1$32e@gagme.wwa.com>
X-Deja-AN: 101578152
approved: boba@wwa.com
sender: boba@gagme.wwa.com
organization: University of Bradford
newsgroups: rec.arts.ascii


Yeah, it's not very arty, but it took me long enough to design and type
it that I felt compelled to share it with someone...
It's a diagram to illustrate a mathematical proof.

Here's an ascii sketch of the "sausage machine":

               ____________          ____________          ____________
              |  ________  |        |  ________  |        |  ________  |
              | |        | |        | |        | |        | |        | |
              | |        | |        | |        | |        | |        | |
            \     /      | |      \     /      | |      \     /      | |
             |   |       | |       |   |       | |       |   |       | |
             |   |       | |       |   |       | |       |   |       | |
            /     \      | |      /     \      | |      /     \      | |
           /       \     | |     /       \     | |     /       \     | |
          |         |    | |    |         |    | |    |         |    | |
Breed     |         |    | |    |         |    | |    |         |    | |
           \       /     | |     \       /     | |     \       /     | |
            \     /      | |      \     /      | |      \     /      | |
             \   /       | |       \   /       | |       \   /       | |
              | |        | |        | |        | |        | |        | |
          ____| |____    | |    ____| |____    | |    ____| |____    | |
Sort     / p   q   r \   | |   / p   q   r \   | |   / p   q   r \   | |
        /____________ \  | |  /____________ \  | |  /____________ \  | |
          | | | | | |    | |    | | | | | |    | |    | | | | | |    | |
          | | | | | |  __|_|____|_|_| |_| |    | |  __|_|_| | | |    | |
          | | | | | | |  _________________|    | | |  ______| | |    | |
          | | | | | | | || |    | |            | | | || |     | |    | |
          | | | |_| |_|_||_|____| |____________|_|_|_||_|___  | |    | |
          | | |___| |___________| |_______________________  | | |    | |
          | |     | | | || |    | |            | | | || | | | | |    | |
          | |_____| |_|_||_|____| |____________|_|_| || |_| |_| |    | |
          |_____________________| |_   ______________||  _| |___|    | |
                      | || |    | | | |        | |    | | | |        | |
               _______| || |    | |_|_|________|_|____| |_| |        | |
              |  _______|| |    |_____________________| |_  |        | |
              | |        | |        | |        | |    | | | |        | |
              | |________|_|________| |________|_|____| | | |        | |
              |  ___________________| |_________________| | |        | |
              | |        | |        | |        | |        | |        | |
              | |        | |        | |        | |        | |        | |
              | |        | |        | |        | |        | |        | |
          ____| |____    | |    ____| |____    | |    ____| |____    | |
         |           |_  | |   |           |_  | |   |           |_  | |
         |             | | |   |             | | |   |             | | |
Copy &   |             |_| |   |             |_| |   |             |_| |
Recycle  |             |___|   |             |___|   |             |___|
         |             |       |             |       |             |
         |_____________|       |_____________|       |_____________|
              | |                   | |                   | |
              | |                   | |                   | |
            __| |__               __| |__               __| |__
           |       |             |       |             |       |
Store      |   A   |             |   B   |             |   C   |
           |_______|             |_______|             |_______|

It's a little messy, but if you squint a bit you can see solid lines and
it all becomes clear. You may have to print it out to view the whole
diagram at once.

It's to illustrate a proof developed in the 20s by the mathematician
Felix Hausorff. It relates to the topology of spheres and how to dissect
a sphere into six pieces which can then be reassembled to give two new
spheres of equal size to the original. If anyone wants the total proof,
just mail me.

Andrew J. Cribbin