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.