--- In

Hyacinthos@yahoogroups.com, "constantxarax"

<constantxarax@y...> wrote:

>

> Construction, by rule and compass, of the equilateral triangle

whose

> vertical projection on the plane is a given triangle.

As a triangle is equilateral if and only if his Steiner

circumellipse is a circle, it follows that, if L is the focal axis

of the Steiner circumellipse of ABC and e the excentricity :

rotate the plane ABC around L with an angle T such as sin(T) = e,

you get the plane of your equilateral triangle.

The sidelength of this equilateral triangle is clearly root(3)*u

where u=semimajor axis.

Friendly. Jean-Pierre