Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!cs.utexas.edu!uunet!yale!Horne-Scott
From: Horne-Scott@cs.yale.edu (Scott Horne)
Newsgroups: comp.misc
Subject: Pie/3?  Why, it's 1.0471975511965977461542144610931676280657...!  :-)
Summary: Hope my mental arithmetic is correct....
Message-ID: <65949@yale-celray.yale.UUCP>
Date: 10 Jul 89 16:24:21 GMT
References: <4859@ficc.uu.net> <1448@mdbs.UUCP>
Sender: root@yale.UUCP
Reply-To: Horne-Scott@cs.yale.edu (Scott Horne)
Organization: Yale University Computer Science Dept, New Haven, CT   06520-2158
Lines: 29
In-reply-to: mm@mdbs.UUCP (Michael MacKenzie)

In article <1448@mdbs.UUCP>, mm@mdbs (Michael MacKenzie) writes:
> 
> There exists a proof about the impossibility of trisecting an arbitrary
> angle with compass & straight edge.  This doesn't seem to stop anyone
> who needs to cut a piece of pie into 3 parts.

Then again, few people attempt to cut a piece of pie with straightedge and
compasses, and few care that the angle be trisected.

For those who do, though, I provide the following

THEOREM.  A pie O with radius OP can be trisected.

Proof.  Construct a circle of radius OP at P.  The circle intersects pie O at
        two points; call them Q and R.  Construct straight lines OQ and OR.
        It may be seen (by the proverbial astute reader :-) ) that thrice
        angle QOR is once angle POP.

That theorem, incidentally, is from the lost fourteenth book of the _Elements_,
which was recently discovered by Betty Crocker in her research in ancient
Greek pastries.

					--Scott

Scott Horne                              Hacker-in-Chief, Yale CS Dept Facility
horne@cs.Yale.edu                         ...!{harvard,cmcl2,decvax}!yale!horne
Home: 203 789-0877     SnailMail:  Box 7196 Yale Station, New Haven, CT   06520
Work: 203 432-6428              Summer residence:  175 Dwight St, New Haven, CT
Dare I speak for the amorphous gallimaufry of intellectual thought called Yale?