Models showing Dandelin theorem.

DANDELIN THEOREM: "Two spheres are inscribed in a right cone and tangent to a plane p if the angle t of the cone is different from the angle f between the axis of the cone and the plane p . If the angles t and f are equals only one sphere is inscribed in the cone and tangent to the plane p. The contact points of the spheres with the plane p are called foci of the conic section. The straight line intersection of the plane p and the plane on which lies the circle made by contact points of the sphere with the cone, is named directrix corresponding to the focus- contact point between the sphere and the plane p. When the angles t and f are equal (the conic saction is a parabola) there is only a focus and a directrix corresponding.". In our models the line generatrix of the conic surface are made up by tightened threads , the circle of contact points between the sphere and the conic surface are realized as envelope of the tangent straight lines.