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).

John Conway