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# Cube Square Inscribing

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.

Cube, Prince Rupert's Cube, Square

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## References

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/.

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Cube Square Inscribing

## Cite this as:

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