Roger Hui wrote: > http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/May2007.html > > What is the size of the largest square that will fit in the unit cube? > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm >
Spoiler below: 3r4*%:2 1.06066 The inscribed square has vertices 1r4 from the corners. This is the Prince Rupert's cube problem. If you take a cube with this edge and push it normal to the inscribed square, it will pass through the unit cube. This is counterintuitive given that it is bigger. I believe this problem really was due to Prince Rupert (of the Rhine), a royalist in the English Civil War, and first published (though not solved) by John Wallis in the late 17th century. It was solved shortly after by Pieter Nieuwland. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
