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

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 John Conway Posts: 2,238 Registered: 12/3/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 17, 1998 12:13 PM

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?]

John Conway

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