TwoFamiliesPonceletPolygonsEllipse::usage=" Poncelet's porism says that whenever a polygon is inscribed in a conical and circumscrbes to another, the polygon must be part of an infinite family of polygons that are all inscribed and circumscribe the same two conicals. References: Wolfram MathWorld: Poncelet's Porism; YouTube: Exploring the Dynamic Geometry and Conservations of the Steiner-Soddy and Harmonic Poncelet Porism, Dan Reznik; Personal ";
In[]:=
Out[]=
Out[]=
The circumference that passes through the tangent points of the circumferences of the Steiner chain (dashed in black) is inscribed in the family of polygons 1 (in orange) whose vertices are the centers of the circles of the Steiner chain and they are on an ellipse. The family of polygons 2 (in dark green) is inscribed to that circle and has its vertices at the tangential points of the circles on the Steiner chain.