Centers of mass of Poncelet polygons, 200 years after
  The locus of the centers of mass of the family of Poncelet polygons, inscribed into a conic $\Gamma$ and circumscribed about a conic $\gamma$, is a conic homothetic to $\Gamma$. 
R. Schwartz, S. Tabachnikov
math.MG math.AG math.HO