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[obm-l] Trisect angle geometrically
Ola Pessoal,
A mensagem abaixo pode ser do interesse de muitas pessoas. Nela o Conway
fala da trisseccao do angulo, um dos problemas classicos da antiguidade.
>From: John Conway <conway@Math.Princeton.EDU>
>To: Craig <jcraigw@msn.com>
>CC: geometry-college@mathforum.org
>Subject: Re: Trisect angle geometrically
>Date: Wed, 21 May 2003 12:31:55 -0400 (EDT)
>
>On 20 May 2003, Craig wrote:
>
> > Can someone lead me to a procedure or proof of how to trisect an angle
> > using geometry? Thank you.
>
> Well, you can't trisect an arbitrarily given angle using ruler and
>compass in the ways presecribed by Euclid, but you can if you use a marked
>ruler. Here's how. Supposing that the ruler has two marks a distance d
>apart, draw a circle of radius d centered at the vertex O of the given
>angle AOB.
>
>
> I hope you can read my figure - but you'll have to imagine that
>circle as passing through A,B,C,Y. Now place your ruler so that it
>passes through B, while one mark X is in the line COA and the
>other one Y is on the circle:-
>
>
> B
> /
> Y /
> /
> -----X----C-------O-------A--------
>
> Then since XY = OY = d the angles OXY and XOY are equal,
>to theta say, and since OY = OB = d (sorry this doesn't look right!)
>the exterior angle OYB = 2theta of this triangle = YBO, and so
>finally the angle AOB, as the exterior angle of triangle XOB
>opposite the two angles OXB = theta and XBO = 2theta, must equal
>3theta.
>
> John Conway
>
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