The master's thesis is based on a theoretical research approach. It focuses on the square peg problem, which asks whether there exist four points on a Jordan curve that form the vertices of a square. This question was first formulated by Otto Toeplitz in 1911, hence it is also known as the Toeplitz conjecture. To this day, the problem remains generally unsolved, although it can be resolved under additional assumptions about the curve (such as smoothness and convexity). In this master's thesis, two instances of the inscribed square problem are presented under two different additional assumptions about the Jordan curve. Following this, we discuss Arnold Emch's article on the existence of an inscribed square in smooth convex Jordan curves and Richard P. Jerrard's article on the existence of an inscribed square in real analytic Jordan curves.
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