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

(In reply to by )

I can't quite follow your placement of the square, but I think it was the same as mine.  If so, this was the same intuition I used to get my result.

Two opposite sides of the square lie across opposite faces of the cube at a distance of 1/4 from the corners of the cube  (forming 45 degree right triangles with the cube).  The other sides are inside the cube and don't form much of an angle with anything except the vertical faces of the cube this angle is about 13.63 degrees.

-Jer

Posted by Jer on 2004-12-26 18:03:58