From: milbrandt@gmx.de
Newsgroups: sci.math.research
Subject: Re: minimum area ellipse containing a given triangle
Date: 15 Oct 1998 08:00:02 -0500

Dennis C. Jespersen <jesperse@o223.nas.nasa.gov> wrote on 13 Oct 1998 18:00:08 -0500:
: 
: Given a triangle, consider the problem of finding the minimum area
: ellipse containing the triangle.  What can one say about the ellipse?
: For example:
: 1. Is this a known problem?
: 2. Existence, uniqueness?
: 3. Presuming 2 holds, can anything be said about the parameters of the
:    ellipse in terms of parameters of the triangle?

This is a special case of the so called Loewner ellipsoid.  

Theorem (K. Loewner): For A be a bounded set (with non-empty interior) in R^d.
Then there exists one and only one ellipsoid E of minimal volume containing A.

The special case of d+1 points in R^d  and its calculation (but also 
calculations for more points) was descriped in
Friedrich Juhnke: Volumenminimale Ellipsoidüberdeckungen, Beiträge zur Algebra
und Geometrie 30 (1990), pp.143-153.

Volker