Date: Nov 7, 1997 6:01 PM
Author: John Conway
Subject: Re: minimum perimeter
On Fri, 7 Nov 1997, Joshua Zucker wrote:
> The question:
> Given an acute triangle, find the inscribed triangle (with one point
> on each side of the original triangle) of minimum perimeter.
> The answer:
> The triangle formed by the feet of the altitudes of the original
> triangle has the smallest perimeter.
> The proof:
> I don't know yet.
> --Joshua Zucker
But I do! This is a well-known theorem, and there's an
easy proof by reflecting the triangle in its sides so as to
convert the problem into a shortest path one (think of light
bouncing around inside a triangle of mirrors).