As shown by Schnirelman (1944), a square can be inscribed in any closed convex curve, although it is not known if this holds true for every Jordan curve (Steinhaus 1999, p. 104). However, a square can be circumscribed about any Jordan curve (Steinhaus 1999, p. 104).
Square Inscribing
See also
Calabi's Triangle, Jordan Curve, Square, Square Packing, Triangle Square InscribingExplore with Wolfram|Alpha
References
Croft, H. T.; Falconer, K. J.; and Guy, R. K. "Inscribing Polygons in Curves." §B2 in Unsolved Problems in Geometry. New York: Springer-Verlag, pp. 51-52, 1991.Schnirelman, L. G. "On Certain Geometrical Properties of Closed Curves." Uspehi Matem. Nauk 10, 34-44, 1944.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 104 and 302, 1999.Referenced on Wolfram|Alpha
Square InscribingCite this as:
Weisstein, Eric W. "Square Inscribing." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SquareInscribing.html