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Re: minimum perimeter
Posted:
Nov 7, 1997 6:01 PM


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 wellknown 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



