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Topic: A Theorem concerning the Trisectors of a Triangle
Replies: 24   Last Post: Nov 10, 1998 12:19 AM

 Messages: [ Previous | Next ]
 Floor van Lamoen Posts: 183 Registered: 12/3/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 17, 1998 1:05 PM

Hi,

John Conway wrote:
>
> On Thu, 17 Sep 1998, Floor van Lamoen wrote:
>

> > Hi,
> >
> > I wrote (on Roussel's triangle):
> >

> > > I have not yet read any notification of the fact that in stead of inside
> > > trisectors also outside trisectors can be used. The equilateral triangle
> > > you get from the outside trisectors and the one you get from the inside
> > > trisectors are reflections of each other over the circumcenter.

> >
> > The first sentence is right, the second isn't. I don't know where I got
> > this from. I'm sorry.

>
> Oh good, because the second sentence misled me into thinking that
> you probably meant something unusual by "outside trisectors" , and I
> spent some fruitless time trying to find out just what. I now take it
> that you just meant the usual external trisectors, namely the lines
> at angles of +- 120 degrees to the internal one. Then what survives
> of your statement is just that the algebraic conjugates of the
> construction also work (as of course they must).
>
> I had in fact already referred to this when I remarked that there
> must be 18 Roussel triangles corresponding to the 18 Morley ones,
> although perhaps they coincide to some extent. [But perhaps that
> was in a message that didn't get sent to you?]

Well, that message was sent to me. But because of the reflection I
found, i didn't think of Morley alikes.
I suppose I have taken the perpendiculars to the internal trisectors
instead, in which case the second sentence of what I wrote is right.

Sorry again!

Best regards,
Floor van Lamoen.

Date Subject Author
9/12/98 Den Roussel
9/12/98 John Conway
9/13/98 Larry Cusick
10/27/98 John Conway
9/13/98 steve sigur
9/14/98 John Conway
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 Richard Guy
9/16/98 Floor van Lamoen
9/16/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 Russell Towle
9/17/98 John Conway
9/17/98 Russell Towle
9/17/98 Douglas J. Zare
9/19/98 Russell Towle
9/20/98 John Conway
9/20/98 John Conway
9/18/98 Antreas P. Hatzipolakis
11/10/98 Den Roussel