In my thesis I present three classical mathematical problems of antiquity. I focus on the problem of doubling the cube, which is examining how can we, given an edge of a cube, construct an edge of a second cube, whose volume is double that of the first. One of the most important cubic plane curves that helps to solve this problem is the cissoid of Diocles, which I describe in greater detail in the present dissertation. Further discussion is given to catacaustics, the curves that are envelopes of reflected rays of a specific beam of rays falling on the cissoid of Diocles. All the stated problems are also modelled using GeoGebra software.
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