Can any rectangle be inscribed in any convex figure?



Can any rectangle be inscribed in any convex figure?
Yes, this follows from a more general result in 


Nielsen and Wright, *Rectangles inscribed in symmetric continua*. Geom. Dedicata 56 (1995), no. 3, 285–297 [MR](http://www.ams.org/mathscinet-getitem?mr=1340790)


(This is reference 4 in the [Wikipedia article](http://en.wikipedia.org/wiki/Inscribed_square_problem) I quoted in my [answer](https://mathoverflow.net/questions/35710/can-any-triangle-be-inscribed-in-any-convex-figure/35715#35715) to your previous question.)


In their terminology, a simple closed curve $C$ is *symmetric* if there exists a point $P\notin C$ such that each straight line through $P$ intersects $C$ in exactly 2 points. This condition is trivially satisfied when $C$ is a boundary of a convex region.


