What is the area of the largest square that can be inscribed on a unit cube (Trott 2004, p. 104)? The answer is 9/8, given by a square with vertices
(1/4, 0, 0), (0, 1, 1/4), (3/4, 1, 1), (1, 0, 3/4), or any configuration equivalent
by symmetry.
In general, let
be the edge of the largest -dimensional cube that fits inside an -dimensional cube, with . Then
(1)
(2)
(3)
(4)
(Croft et al. 1991, p. 53). For larger , little is known.
be the edge of the largest 
-dimensional cube that fits inside an 
-dimensional cube, with 
. Then
, little is known.
