Abstract
The article reveals the trajectory of organizing and teaching a facultative course in order to familiarize students with non-Euclidean geometries in schools. It shows why students should be introduced to non-Euclidean geometries in schools, and what goals can be achieved by teaching non-Euclidean geometries. The most important aspect is the trajectory of the organization of the optional course. When organizing a facultative course, it is indicated what topics to choose, how many hours to allocate, and the program of the facultative course is developed.
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