THE CONCEPT OF SYMMETRY IN GEOMETRY
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Abstract
This article provides a comprehensive examination of symmetry in geometry, delineating its definition as invariance under transformations such as reflections, rotations, translations, and glide reflections. It categorizes fundamental types, illustrates their manifestations in common shapes and polygons, and explores advanced applications in group theory, the Erlangen Program, and physics via Noether's Theorem. The discussion underscores symmetry's role in balancing proportions, pattern recognition, and foundational principles across mathematical and physical domains, offering pedagogical insights for geometric education.
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References
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