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The Square Peg Problem, first posed by O. Toeplitz in 1911, asks whether every Jordan curve in the plane contains the four vertices of a square. Although the original problem has not been proved yet, there have been affirmative solutions to that problem with various restricted conditions either on the vertices or on the curve. In this paper, we study the Square Peg Problem where we look for squares with lattice vertices. We study southeast curves and in particular those of pure width. We prove most cases of the Lattice Square Peg conjecture for pure width southeast lattice curves and study the conjecture with some small widths.
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Tu, Zhexiu, "Square Peg Problem on Lattice Plane" (2011). Senior Projects Spring 2011. 87.
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