The inscribed square problem asks for the existence of four points on the Jordan curve that form vertices of a square. Even though that problem remains open, the inscribed rectangle problem has been solved using elementary topology. The analysis of the inscribed rectangle problem and the theory we need to solve it are the central themes of this thesis. At the beginning, we solve two special examples of the inscribed rectangle problem, then we present the quotient spaces and pay more attention to the Jordan curves. In the end, we combine the acquired knowledge into a solution to the inscribed rectangle problem.
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