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Three Cuts and Seven Pieces

Date: 01/18/99 at 23:51:55
From: Jordan Caviness
Subject: Dividing a circle

Is there any way that you can cut a pie into seven pieces with just 
three straight cuts? I don't think so, unless when you stop at the 
edge of the pie you can go back across it, just at a different angle 
and count that as one cut. And would that cut be considered straight. 
Please help.


Date: 01/19/99 at 12:32:40
From: Doctor Rob
Subject: Re: Dividing a circle

Thanks for writing to Ask Dr. Math!

Yes, this can be done.

Around the outside of the pie pick five points A, B, C, D, and E.
Cut A to D and B to E. Call the intersection of these cuts P. Pick
a sixth point F on the outside of the pie between E and A, but not on
the line CP extended. Cut C to F. Here's a rough diagram:

                 ,-'           `-.
             B ,'                 `. C
             ,'\                    /.
            /   \                  /  \
           /     \                /    \
          ,       \              /      .
          |        \ P          /       |
        A +---------o----------/--------+ D
          |          \        /         |
          .           \      /          ,
           \           \    /          /
            \           \  /          /
             `.          \/         ,'
               `.        /\       ,'
                 `-._   /  \  _,-'
                      F      E

See the seven pieces?

If you are allowed to rearrange the pieces after the second cut, you 
can even make eight pieces.

- Doctor Rob, The Math Forum   
Associated Topics:
Elementary Circles
Elementary Geometry
Elementary Puzzles
Elementary Two-Dimensional Geometry
Middle School Conic Sections/Circles
Middle School Geometry
Middle School Puzzles
Middle School Two-Dimensional Geometry

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