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From: mjm@eleazar.dartmouth.edu (Michael McClennen)
Newsgroups: comp.misc
Subject: Re: More on tri vs. bi
Keywords: mathematics
Message-ID: <14266@dartvax.Dartmouth.EDU>
Date: 6 Jul 89 23:35:47 GMT
References: <4859@ficc.uu.net>
Sender: news@dartvax.Dartmouth.EDU
Reply-To: mjm@dartmouth.edu (Michael McClennen)
Organization: Dartmouth College, Hanover, NH
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In article <4859@ficc.uu.net> jeffd@ficc.uu.net (jeff daiell) writes:
>I've been following the discussion of trinary computers,
>which brought to mind another question: has anyone ever
>succeeded in trisecting an angle?  

To (hopefully) tie up a trivial but interesting thread, the answer is:

Sure.  The trisection of 60 degrees, for instance, is 20 degrees.

Oh, you meant the general case!  Well, how closely can you measure the angle?
If you know the exact angle you wish to trisect, simply find a pocket
calculator and divide by three.  If not, well, your answer will be as accurate
as the protractor you use to measure it...

Oh, you meant using only a straightedge and compass!  Well, certain angles can
certainly be trisected by this method (60 degrees, for instance), but there
are many angles that cannot.  The proof that I have seen for this assertion
involves field theory (a branch of abstract algebra), and will probably be
found in any standard introduction to the subject, for it is a basic exercise.

All rumours of a general method for trisecting an angle using only an unmarked
straightedge and compass are false!  Note, however, that if one allows oneself
to make marks on the straightedge, the problem becomes solvable, and is indeed
not that difficult.


Michael McClennen
mjm@dartmouth.edu