Square Inscribing

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).

See also

Calabi's Triangle, Jordan Curve, Square, Square Packing, Triangle Square Inscribing

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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.

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Square Inscribing

Cite this as:

Weisstein, Eric W. "Square Inscribing." From MathWorld--A Wolfram Web Resource.

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