The Largest k-Ball in an n-Box

We are interested in finding the maximal radius that a k-dimensional Euclidean ball can attain while being inscribed inside an n-dimensional box, where k=1,...,n. We will also investigate how the ball  should be situated within the box in order to achieve this maximal radius.  This problem was first attempted by Everett, Stojmenovic, Valtr, and  Whitesides in 1998, where they derived a formula for the maximal radius. In this talk, we will rederive their result and give the equations of the  k-dimensional affine subspaces that contain these maximal radius Euclidean  balls.