Can any triangle be inscribed in any convex figure? i.e. given a convex figure and a triangle can we transpose and scale and rotate that triangle so that its vertices are on the boundary of the convex figure?



Can any triangle be inscribed in any convex figure?
A more general result is known: if $C$ is any Jordan curve and $T$ is a triangle then there exists a triangle similar to $T$ inscribed in $C.$ Moreover, the vertices of such triangles are dense in $C.$ See the references in the Wikipedia article on the [Inscribed Square Problem](http://en.wikipedia.org/wiki/Inscribed_square_problem#Variants_and_generalizations).


