THE CONCEPT OF SYMMETRY IN GEOMETRY

Djurabayev Oybek Urambayevich

doi:10.55640/

Authors

Djurabayev Oybek Urambayevich Mathematics teacher at the Academic Lyceum of Turin Polytechnic University in Tashkent

DOI:

https://doi.org/10.55640/

Keywords:

symmetry, reflectional symmetry, rotational symmetry, translational symmetry, glide reflection, regular polygons, symmetry group, Erlangen Program, Noether's Theorem, geometric invariance

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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