Illuminating high school students with some interesting non-euclidean geometries in the plane

Global trends in mathematics education show that modern teaching methods are rapidly evolving at the national, regional, and global levels. In this regard, teaching non-Euclidean geometry concepts in schools can be essential in developing students' spatial imagination and enhancing scientific inquiry competencies. This paper aims to engage and increase students' interest in geometry science by introducing the fundamental concepts of several non-Euclidean geometries. With this aim, we will first give you a modern definition of geometry and move towards the exciting and fun world of non-Euclidean geometry. Of course, remember that the target audience we will talk about these issues is talented students in secondary and high schools.AMS Subject Classification (2020): Primary: 51K99; Secondary: 97G10

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