[comp.misc] Pie/3? Why, it's 1.0471975511965977461542144610931676280657...! :-)

Horne-Scott@cs.yale.edu (Scott Horne) (07/10/89)

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
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