I consider all the convex bodies of constant width in $\mathbb{R^2}$ (to fix ideas I take the width equal 1 )
I consider that all these bodies are centered in O( O is the Origine the Cartesian coordinate system in |R^2)
my question is :
what is the upper bound of the Hausdorff distance between the disk and any convex body of constante width (width=1)?