Dear Jean-Pierre

Very nice remark about the minimum property of the focal axis of the Steiner

ellipses.

Have we some generalisation with the minimum of the function defined on the

space of affine lines:

L --> p.d(A, L)� + q.d(B, L)� + r.d(C, L)� where the sum p+q+r is not equal

to 0.

Obviously, the minimum line is on the point with barycentrics (p, q, r).

It would be nice if the minimum line is the focal axis of the inconic (or

circcumconic) with center (p, q, r)?

Friendly

Francois

On Thu, Mar 10, 2011 at 1:32 PM, Etienne Rousee <etienne@...> wrote:

>

>

> Le 08/03/2011 19:09, jpehrmfr a �crit :

>

> >> Is the line L, minimizing the sum of

> >> the squares of the distance from A,B,C

> >> to L, always a median of ABC ?

> >

> > No, this line is the focal axis of the Steiner ellipses

>

> Yes, and is the line maximizing the sum the other

> axis of the Steiner ellipse ?

> I was mistaken because I experimented whis the sum

> of the distances and forgot the squares.

> In this case, it seems near a median.

>

> --

>

> Etienne

>

>

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