Given a unit cube, what is the largest square that can be placed completely inside the cube?

Let ABCD be the bottom face & EFGH be the top face of the cube.(edges of the other faces are AE,BF,CG,DH).   Let P be the mid point of BF & Q be the mid point of DH.   Now APGQ forms a square.  side of this new square=AP= sqrt(AB*AB+BP*BP)= sqrt(1*1+0.5*0.5)=sqrt(1.25).

Posted by suman on 2005-01-29 19:52:33