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.

Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, 1991.

Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.

CITE THIS AS:

Weisstein, Eric W. "Cube Square Inscribing." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CubeSquareInscribing.html