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. 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/
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