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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.

Thanks,
Jordan
```

```
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
http://mathforum.org/dr.math/
```
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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