From - Tue Jun  1 10:45:09 1999
From: xpolakis@hol.gr (Antreas P. Hatzipolakis)
Newsgroups: rec.puzzles,sci.math
Subject: Re: Trisecting a line
Date: 30 May 1999 19:36:57 GMT
Organization: Crete
Lines: 27
Message-ID: <xpolakis-2708561551410001@athe530-d079.otenet.gr>

In article <7iot2q$q27$1@news.fas.harvard.edu>, Noam D. Elkies
<elkies@mathematics.harvard.edu> wrote (in part):

> [I found this myself some 20 years ago, but imagine that it's a

And some 10 years ago I read this problem by Noam D. Elkies:

For plane triangle A_1A_2A_3, call two circles within the triangle companion 
incircles if they are the incircles of two triangles formed by dividing
A_1A_2A_3 into two smaller triangles by passing a line through one of the 
vertices and some point on the opposite side.
(a) Show that any chain of circles C_1,C_2,.... such that C_i, C_i+1 are
companion incircles for every i consists of at most six distinct circles.
(b) Give a ruler and compass construction for the unique chain which
has only three distinct circles.
(c) For such a chain of three circles show that the three subdividing
lines are concurrent.

I guess he (:the  problem's author) is you, unless it was written by
another man of that name cf.

   Actually, Homer was not written by Homer but by another man of that name.


:-))

Antreas