TOPICS
Search

Cube Square Inscribing


CubeSquareInscribing

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 f(m,n) be the edge of the largest m-dimensional cube that fits inside an n-dimensional cube, with m<n. Then

f(1,n)=sqrt(n)
(1)
f(2,3)=3/4sqrt(2)
(2)
f(2,2n)=sqrt(n)
(3)
f(2,2n+1)=sqrt(n+1/8)
(4)

(Croft et al. 1991, p. 53). For larger m, little is known.


See also

Cube, Prince Rupert's Cube, Square

Explore with Wolfram|Alpha

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/.

Referenced on Wolfram|Alpha

Cube Square Inscribing

Cite this as:

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

Subject classifications