# INSCRIBED SQUARES IN PLANE CURVES

@article{Jerrard1961INSCRIBEDSI, title={INSCRIBED SQUARES IN PLANE CURVES}, author={Richard Jerrard}, journal={Transactions of the American Mathematical Society}, year={1961}, volume={98}, pages={234-241} }

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by x = x(t), y = y(t). These are real analytic periodic functions with period T. In the following paper it is shown that in a certain definite sense, exactly an odd number of squares can be inscribed in every such curve which does not contain an infinite number of inscribed squares. This theorem is similar to the theorem of Kakutani [1] that there exists a circumscribing cube around…

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Communicated by R. H. Bing, May 20, 1959 Let E be a euclidean ^-space with a rectangular cartesian coordinate system (x) — (xi, • • • , xn), and let (y) be any system which is a rotation of (x). Let…